Inverse Matrices and Their Properties
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- Опубликовано: 19 июл 2024
- We learned about matrix multiplication, so what about matrix division? There is no such thing! But we can multiply a matrix by its inverse, which is kind of like multiplying a number by its reciprocal, to cancel it out, which with matrices will yield the identity matrix. So how do you find an inverse matrix? Let's learn how!
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instead of that labourious way you did for finding the inverse of a 3x3 you can just create an augmented matrix with A and its identity like [A | I], then row reduce until the identity matrix is on the left side, the matrix on the right side is the inverse of A.
thanks for letting us know a different method. personally i would rather do anything than something that involves row reducing loll
@@hannahakimi1377 so I came here because I'm currently being forced to use row reduction for school in order to get the inverse of a matrix
Yeah and I hate that one because it is longer than this.😩
That takes more effort though, this method is efficient
Verified True. Thanks
You are truly a life saver. You helped me through organic chemistry and now linear algebra. I wish u were my prof👑
" thank you very much" is not enough to describe my gratitude.
Ive got a final tomorrow, never understood any of what was said in class. I have only reviewed for 2 hours using your videos and I'm already caught up with everything up to determinants. On to eigenvalues and vectors and then vector geometry. Thank you professor dave!
Same here man, you're probably in my class 😂
@@Luckster2322 uofr 122?
Professor Dave, you are a LEGEND. I missed almost two weeks worth of stuff from my six-week course, fearing that I'd fail the exam because it was impossible to catch up. And here you are, making me finally gain a proper grasp on these concepts in less time than it'd take for me to even get to school.
Thank you so much for your quality content!!
I am from India and I've been your fan for a long time......I just wonder why your videos don't get a millions of likes....
Please spread the word!
@@ProfessorDaveExplains Obviously...
because most of people around us like to have quantity and entertainment not quality. They want quick solutions, but not like to understand or study the concepts to solve it by themselves.
thank you so much. i am first year Civil engineering BE and i have ADHD . i find everything so boring and unessecary but now i am loving to practice. i have till 6 may to study. i have calc1 algebra2 finals the same day. and thermo on the 10th of may. you saved my life and time. thank you very much.
how did they go?
The proof of inverse of A is so great !
It helps a lot and a lot to study matrix.
Thank you, Prof. Dave!
You covered 15 pages of my textbook in 10 minutes...this guy is a math god
Literally, why is formats and teaching styles like this not the norm.
Helped me through organic chem when I was doing pharmacy, and now maths when I'm doing physics. You're really saving my studies!
Hey fam, I hope that you and your loved ones are well. I would like to ask you the most important question ever asked:
Who is Jesus? Not who is He to you. Rather, who is He really?
Jesus is the Son of God, who came to the world as a man. He lived a perfect and sinless life . Even though He was perfect and sinless, on the cross of Calvary God wrathfully punished Him for the sins of the world. 3 days later He rose from death. Now He is seated at the right hand of God, ruling as King over Heaven and Earth.
On the judgment day He will judge you, me and every human being that has ever lived. Those who believed in Him will enter eternal joy with Him, but those who did not believe in Jesus will be sent to eternal condemnation.
So turn from your sins and believe in the Jesus. Believe and hope that you can be forgiven for all your sins because of His death and resurrection. He took your place in Hell, so that if you submit to Him as your Lord and God, you can be forgiven and take His place in heaven- you will be made sinless and perfect before the Holy Father. He'll also give you a new heart and mind that can love and obey Him.
Jesus lives so that you can have true life and freedom, and most importantly so that you can have an eternally peaceful relationship with God.
You are dead, and Jesus is your only Hope of life by reading The Bible. Start in Matthew, and try and read it through to The book of Revelation. Spend at least 15 minutes in a private place to read it. Read the Bible over and over again. The Creator of The universe, nature and all creation, has made Himself more clearly known through The Bible, as it is the only perfect, unchanging and authoritative revelation of God. You know there is an Almighty and Glorious God when you look at the universe and nature, but you can only know who He is by reading the Bible.
Bible link for YOU: my.bible.com/bible/111/MAT.1.NIV
Acts 15:11
”On the contrary, we believe it is through the grace of the Lord Jesus that we are saved, just as they are."
Ephesians 1:7
”In Him, we have redemption through His blood, the forgiveness of our trespasses, according to the riches of His grace"
Ephesians 2:8
”For it is by grace you have been saved through faith, and this not from yourselves; it is the gift of God,”
John 11:25-26: "Jesus said to her, 'I am the resurrection and the life. The one who believes in me will live, even though they die; and whoever lives by believing in me will never die. Do you believe this?'
1 Corinthians 6:14: "And God raised the Lord and will also raise us up by his power."
Romans 6:9: "We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him."
bible.knowing-jesus.com/topics/Christ-Is-Lord
Source: bible.knowing-jesus.com/topics/Christ-Overcoming
Revelations 19:16
"And on His robe and on His thigh He has a name written, “KING OF KINGS, AND LORD OF LORDS.”
Acts 10:36
"The word which He sent to the sons of Israel, preaching peace through Jesus Christ (He is Lord of all)"
John 16:33
"I have told you all this so that you may have peace in me. Here on earth you will have many trials and sorrows. But take heart, because I have overcome the world.”
I am glad we have computer algebra systems these days 😳😅
For 3*3 matrixes or any large matrix you can just use identity matrix to find inverse, you dont need a cofactor method.
I've so confused about inverse matrix for so long and couldn't find any lecture so convenienced, thank you so much
well covered & explained, thankyou.
Thank you for this....exactly what I needed!!
Very nice! Clear and concise!
Great work Dave!
You are the best of all instructors on u-tube. God bless you.
Hey Dave, I'm loving your channel. just figured I'd mention that the dot product video doesn't seem to be in the linear algebra playlist.
Thank you very much Prof . It was really helpful
Thank you very much, such a great explanation👏
Very simple and amazing explanation 👏👌👍
Thanks for the lesson!!!
Very helpful way better than my own professor thanks dave please make nore vids for linear algebra
Love u professor....I wish I was taught by you. You teach every subject very well.
Hey fam, I hope that you and your loved ones are well. I would like to ask you the most important question ever asked:
Who is Jesus? Not who is He to you. Rather, who is He really?
Jesus is the Son of God, who came to the world as a man. He lived a perfect and sinless life . Even though He was perfect and sinless, on the cross of Calvary God wrathfully punished Him for the sins of the world. 3 days later He rose from death. Now He is seated at the right hand of God, ruling as King over Heaven and Earth.
On the judgment day He will judge you, me and every human being that has ever lived. Those who believed in Him will enter eternal joy with Him, but those who did not believe in Jesus will be sent to eternal condemnation.
So turn from your sins and believe in the Jesus. Believe and hope that you can be forgiven for all your sins because of His death and resurrection. He took your place in Hell, so that if you submit to Him as your Lord and God, you can be forgiven and take His place in heaven- you will be made sinless and perfect before the Holy Father. He'll also give you a new heart and mind that can love and obey Him.
Jesus lives so that you can have true life and freedom, and most importantly so that you can have an eternally peaceful relationship with God.
You are dead, and Jesus is your only Hope of life by reading The Bible. Start in Matthew, and try and read it through to The book of Revelation. Spend at least 15 minutes in a private place to read it. Read the Bible over and over again. The Creator of The universe, nature and all creation, has made Himself more clearly known through The Bible, as it is the only perfect, unchanging and authoritative revelation of God. You know there is an Almighty and Glorious God when you look at the universe and nature, but you can only know who He is by reading the Bible.
Bible link for YOU: my.bible.com/bible/111/MAT.1.NIV
Acts 15:11
”On the contrary, we believe it is through the grace of the Lord Jesus that we are saved, just as they are."
Ephesians 1:7
”In Him, we have redemption through His blood, the forgiveness of our trespasses, according to the riches of His grace"
Ephesians 2:8
”For it is by grace you have been saved through faith, and this not from yourselves; it is the gift of God,”
John 11:25-26: "Jesus said to her, 'I am the resurrection and the life. The one who believes in me will live, even though they die; and whoever lives by believing in me will never die. Do you believe this?'
1 Corinthians 6:14: "And God raised the Lord and will also raise us up by his power."
Romans 6:9: "We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him."
bible.knowing-jesus.com/topics/Christ-Is-Lord
Source: bible.knowing-jesus.com/topics/Christ-Overcoming
Revelations 19:16
"And on His robe and on His thigh He has a name written, “KING OF KINGS, AND LORD OF LORDS.”
Acts 10:36
"The word which He sent to the sons of Israel, preaching peace through Jesus Christ (He is Lord of all)"
John 16:33
"I have told you all this so that you may have peace in me. Here on earth you will have many trials and sorrows. But take heart, because I have overcome the world.”
Thank you! 💯... Very well explained👏👏👏
Best explanation ever! Thank you!!
This way doctored only for us inclined to math people ,say thanks profe David please!
Thnx prof❤️...love form" INDIA"🇮🇳🇮🇳❤️❤️
Sir is angle AOB same as BOA.I feel that the sign of the angle changes bcuz when we measure an angle we measure it from initial to final ray right!then while measuring AOB angle if we move in clockwise then obviously while measuring BOA that must be antivlockwise .Am I correct sir??
Great video! Thanks!
this dude saved my math grade in 10 minutes, respect bro
You release this after my math IA was due, damn
Best explanation of Inverse Matrices on youtube, thank you sir!
Hey fam, I hope that you and your loved ones are well. I would like to ask you the most important question ever asked:
Who is Jesus? Not who is He to you. Rather, who is He really?
Jesus is the Son of God, who came to the world as a man. He lived a perfect and sinless life . Even though He was perfect and sinless, on the cross of Calvary God wrathfully punished Him for the sins of the world. 3 days later He rose from death. Now He is seated at the right hand of God, ruling as King over Heaven and Earth.
On the judgment day He will judge you, me and every human being that has ever lived. Those who believed in Him will enter eternal joy with Him, but those who did not believe in Jesus will be sent to eternal condemnation.
So turn from your sins and believe in the Jesus. Believe and hope that you can be forgiven for all your sins because of His death and resurrection. He took your place in Hell, so that if you submit to Him as your Lord and God, you can be forgiven and take His place in heaven- you will be made sinless and perfect before the Holy Father. He'll also give you a new heart and mind that can love and obey Him.
Jesus lives so that you can have true life and freedom, and most importantly so that you can have an eternally peaceful relationship with God.
You are dead, and Jesus is your only Hope of life by reading The Bible. Start in Matthew, and try and read it through to The book of Revelation. Spend at least 15 minutes in a private place to read it. Read the Bible over and over again. The Creator of The universe, nature and all creation, has made Himself more clearly known through The Bible, as it is the only perfect, unchanging and authoritative revelation of God. You know there is an Almighty and Glorious God when you look at the universe and nature, but you can only know who He is by reading the Bible.
Bible link for YOU: my.bible.com/bible/111/MAT.1.NIV
Acts 15:11
”On the contrary, we believe it is through the grace of the Lord Jesus that we are saved, just as they are."
Ephesians 1:7
”In Him, we have redemption through His blood, the forgiveness of our trespasses, according to the riches of His grace"
Ephesians 2:8
”For it is by grace you have been saved through faith, and this not from yourselves; it is the gift of God,”
John 11:25-26: "Jesus said to her, 'I am the resurrection and the life. The one who believes in me will live, even though they die; and whoever lives by believing in me will never die. Do you believe this?'
1 Corinthians 6:14: "And God raised the Lord and will also raise us up by his power."
Romans 6:9: "We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him."
bible.knowing-jesus.com/topics/Christ-Is-Lord
Source: bible.knowing-jesus.com/topics/Christ-Overcoming
Revelations 19:16
"And on His robe and on His thigh He has a name written, “KING OF KINGS, AND LORD OF LORDS.”
Acts 10:36
"The word which He sent to the sons of Israel, preaching peace through Jesus Christ (He is Lord of all)"
John 16:33
"I have told you all this so that you may have peace in me. Here on earth you will have many trials and sorrows. But take heart, because I have overcome the world.”
thank you professor dave very much,you video is very helpful for me
Very good explanation. And you look so natural. Thanks from the end of the world
Very clear and didactic.
my godness you have reached almost 1 mil subs. Professor Dave Explains
ur teaching level is so easy and better explaination i love u from india
thank youuuu so much. this helped a lot.
I didn't understand why until this video you are great
fast and practical...thanksss
I think at the end sir asked to find the inverse but the answer given is of the adjoint.....but the explanation is outstanding I loved it
In that question inverse was equal to the adjoint
@@bhargav96 ohh I see...thanks a lot
hi Prof Dave: hope you can have a video on Singular Value Decomposition SVD soon. thanks.
Hey fam, I hope that you and your loved ones are well. I would like to ask you the most important question ever asked:
Who is Jesus? Not who is He to you. Rather, who is He really?
Jesus is the Son of God, who came to the world as a man. He lived a perfect and sinless life . Even though He was perfect and sinless, on the cross of Calvary God wrathfully punished Him for the sins of the world. 3 days later He rose from death. Now He is seated at the right hand of God, ruling as King over Heaven and Earth.
On the judgment day He will judge you, me and every human being that has ever lived. Those who believed in Him will enter eternal joy with Him, but those who did not believe in Jesus will be sent to eternal condemnation.
So turn from your sins and believe in the Jesus. Believe and hope that you can be forgiven for all your sins because of His death and resurrection. He took your place in Hell, so that if you submit to Him as your Lord and God, you can be forgiven and take His place in heaven- you will be made sinless and perfect before the Holy Father. He'll also give you a new heart and mind that can love and obey Him.
Jesus lives so that you can have true life and freedom, and most importantly so that you can have an eternally peaceful relationship with God.
You are dead, and Jesus is your only Hope of life by reading The Bible. Start in Matthew, and try and read it through to The book of Revelation. Spend at least 15 minutes in a private place to read it. Read the Bible over and over again. The Creator of The universe, nature and all creation, has made Himself more clearly known through The Bible, as it is the only perfect, unchanging and authoritative revelation of God. You know there is an Almighty and Glorious God when you look at the universe and nature, but you can only know who He is by reading the Bible.
Bible link for YOU: my.bible.com/bible/111/MAT.1.NIV
Acts 15:11
”On the contrary, we believe it is through the grace of the Lord Jesus that we are saved, just as they are."
Ephesians 1:7
”In Him, we have redemption through His blood, the forgiveness of our trespasses, according to the riches of His grace"
Ephesians 2:8
”For it is by grace you have been saved through faith, and this not from yourselves; it is the gift of God,”
John 11:25-26: "Jesus said to her, 'I am the resurrection and the life. The one who believes in me will live, even though they die; and whoever lives by believing in me will never die. Do you believe this?'
1 Corinthians 6:14: "And God raised the Lord and will also raise us up by his power."
Romans 6:9: "We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him."
bible.knowing-jesus.com/topics/Christ-Is-Lord
Source: bible.knowing-jesus.com/topics/Christ-Overcoming
Revelations 19:16
"And on His robe and on His thigh He has a name written, “KING OF KINGS, AND LORD OF LORDS.”
Acts 10:36
"The word which He sent to the sons of Israel, preaching peace through Jesus Christ (He is Lord of all)"
John 16:33
"I have told you all this so that you may have peace in me. Here on earth you will have many trials and sorrows. But take heart, because I have overcome the world.”
I’m a bit confused with the comprehension check. I get the the adjugate to be the answer that you’ve given as the inverse matrix. Isn’t there then a step to divide by the the determinant of the original matrix which I make to be -13
the determinant is 1 hence the inverse looks like the adjucated matrix
Thank you Professor
Didnt got how yomultiplied 1/-1 into the adjoint A , you just made a shortcut and wrote it, can you please explain how to multiply because 1/-1 gives a zero ?
You are the best thank you💐💐💐
How cool!! Thanks!!
Awesome Professor Dave❤❤❤❤
loved this video
Thank you professor
note if you are studying in french it’s called: une matrice inversée for an inverse matrix and fonction réciproque for an inverse function
thanks
Thanks alot ❤
Thank you so much for everything! I now know physics & mathematics in a very high level, and I find it very interesting, I'm 15 so what we learn at school is a mere bagatelle...
Matrices exam tomorrow ! thanks
Thank you sir
I guess lectures are just meant to complicate things😔I am happy student now ❣Thanks Prof.
Can’t you just use gauss Jordan elimination to find A^-1? (Start with one matrix n x 2n, A and I adjoined. Eliminate until you have I x A^-1)
when you did the first determinant on the 3x3 matrix why didnt you multiply by the numbers you did the determinats of
Thanks!
This is what happens when you stop gatekeeping mathemathics with ridicolous notation
Well explained...but pls indeed explanation of original matrix wen the inverse is given.thank u
I love u so much. Here have my subscription!
5:00
matrices
-addition
-substraction
-multiplication
-*determinants
-*inverses
amazing video
Thank you sir you're my first choice
Thanks ❤
Ur the best thank you
thank you
Great explanation, reading from the course books are not clear and takes too much time
If we know that method do we need row operation?
I love the intro so fun hahah
Thanks professor it's really halpern ful. ..
Sir my math portin of physical chemistry is so week Sir give some advice. ....
for step 4, why is it 1 times determinant of 1, minus 2 times determinant of 2?
Basically, where does the minus come from?
Hey fam, I hope that you and your loved ones are well. I would like to ask you the most important question ever asked:
Who is Jesus? Not who is He to you. Rather, who is He really?
Jesus is the Son of God, who came to the world as a man. He lived a perfect and sinless life . Even though He was perfect and sinless, on the cross of Calvary God wrathfully punished Him for the sins of the world. 3 days later He rose from death. Now He is seated at the right hand of God, ruling as King over Heaven and Earth.
On the judgment day He will judge you, me and every human being that has ever lived. Those who believed in Him will enter eternal joy with Him, but those who did not believe in Jesus will be sent to eternal condemnation.
So turn from your sins and believe in the Jesus. Believe and hope that you can be forgiven for all your sins because of His death and resurrection. He took your place in Hell, so that if you submit to Him as your Lord and God, you can be forgiven and take His place in heaven- you will be made sinless and perfect before the Holy Father. He'll also give you a new heart and mind that can love and obey Him.
Jesus lives so that you can have true life and freedom, and most importantly so that you can have an eternally peaceful relationship with God.
You are dead, and Jesus is your only Hope of life by reading The Bible. Start in Matthew, and try and read it through to The book of Revelation. Spend at least 15 minutes in a private place to read it. Read the Bible over and over again. The Creator of The universe, nature and all creation, has made Himself more clearly known through The Bible, as it is the only perfect, unchanging and authoritative revelation of God. You know there is an Almighty and Glorious God when you look at the universe and nature, but you can only know who He is by reading the Bible.
Bible link for YOU: my.bible.com/bible/111/MAT.1.NIV
Acts 15:11
”On the contrary, we believe it is through the grace of the Lord Jesus that we are saved, just as they are."
Ephesians 1:7
”In Him, we have redemption through His blood, the forgiveness of our trespasses, according to the riches of His grace"
Ephesians 2:8
”For it is by grace you have been saved through faith, and this not from yourselves; it is the gift of God,”
John 11:25-26: "Jesus said to her, 'I am the resurrection and the life. The one who believes in me will live, even though they die; and whoever lives by believing in me will never die. Do you believe this?'
1 Corinthians 6:14: "And God raised the Lord and will also raise us up by his power."
Romans 6:9: "We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him."
bible.knowing-jesus.com/topics/Christ-Is-Lord
Source: bible.knowing-jesus.com/topics/Christ-Overcoming
Revelations 19:16
"And on His robe and on His thigh He has a name written, “KING OF KINGS, AND LORD OF LORDS.”
Acts 10:36
"The word which He sent to the sons of Israel, preaching peace through Jesus Christ (He is Lord of all)"
John 16:33
"I have told you all this so that you may have peace in me. Here on earth you will have many trials and sorrows. But take heart, because I have overcome the world.”
@@carsanovadidrifto800Go away, you bot!
Laplace
Awesome 😎
PROFESSOR PLEASE CAN YOU HELP ME WITH PROBABILITY
How does the checkerboard pattern work for 4×4 anad 6x6 matrices?
Good question. The upper-left entry is always positive, and the main diagonal is always positive.
So for a 4x4 matrix, the pattern is:
[ +, -, +, -]
[ -, +, -, +]
[ +, -, +, -]
[ -, +, -, +]
wow you took a 2 hour lecture that the professor wasn't explaining well and explained everything so effectively in a 12 minute video.
Prof, could we just use Gauss-Jordan Elimination to get the inverse of a 3x3 matrix?
yes
Yes.
GJE is generally a more computationally-efficient method if you are given a matrix where the rows are easy to reduce, if you can find the right path through the row operations. The method of minors, cofactors and determinants by contrast is more straight-forward without requiring you to think about the contents of each row to find the strategic row operations.
where is the video for the assignment
this was great but it doesn't seem to work for all 3x3 matrices. I had a question come up in a past paper
(which I will put below) and this method did not work for that question.
1 2 1
3 -4 -2
5 3 5
if someone can show me a solution to this, that would be much appreciated x
It is possible to use GJE on this matrix. Here are the steps:
R2 := R2 - 3*R1
R1: = R1 + R2/5
R3:= R3 - 5*R1
R2 := R2/-10
R3:= R3 - 3*R2
R3:=R3*2/7
R2:= R2 - R3/2
The inverse ends up being:
[2/5, 1/5, 0]
[5/7, 0, -1/7]
[-29/35, -1/5, 2/7]
When I first tried it, I ended up making the 3rd entry of the 3rd row equal to zero, which led me astray. There was still a second entry in this row, so I didn't eliminate the row completely, which is a sign that either two rows are redundant or contradictory (which wasn't the case). If this ever happens, where you eliminate the wrong entry of the row (but one of the other entries still remains), just swap two rows, so the last entry standing is in the correct place.
I can confirm that I got the same method with the method of minors, cofactors, adjuncts and determinants. As long as the original matrix's determinant is not zero, you can always use this method to find its inverse.
God bless you!!
GOD, I Love that Intro...
shows the relations of dot and cross product by equation
How do I find the original matrix from the inverse
Thank you math jesus
you explain it well, I know it is useful, but I freaking hate inverse Matrices...I think the least intuitive operation in all of mathematics
Thanks for saving my grade
Professor, how's the merch sale going on?
terrible! no one wants them :(
@@ProfessorDaveExplains I'm sorry to hear that.
RUclips merch is mostly terrible at selling I'll admit. Only the big boys with over 10 mill subs are able to dominate merch sale.
Many other RUclipsrs with as many subs as you suffer similarly.
But once you grow, you'll sell it for sure.
I'm broke, so sorry I can't support you though.
But thank you for your videos.
One question though, why isn't this video monetised?
yep i think things will be different in a year or two! all my videos are monetized, does it say differently somewhere?
@@ProfessorDaveExplains I dunno , there just happen to be no ads on this video. I'm not sure if that's how it works. But there's no ad, and no yellow and mark on the video bar.
Otherwise, I always watch whole 30 second ads to support you
The best for the inverse.. God of MATRIX 🙏🙏🙏🙏
Well
I find it strange that you say "A inverse is not the reciprocal, because there is no such thing as matrix division". I was thinking that it IS the reciprocal of the matrix abstraction. Is it not?
I think he meant it’s not just dividing each element with the corresponding element of another matrix ( a/b ), that’s how I interpreted that line
One _could_ think of an inverse matrix as being similar to a "matrix division". But there are reasons why we often _don't_ think of it as division. For one, there are plenty of matrices which don't have inverses. But more importantly, matrix multiplication is not commutative. So we would need to make sense of "dividing on the left" and "dividing on the right" - because what side you do things on _matters._ And we don't typically think of division as being "sided".
We will first find something called the "Matrix of Minors".
I thought that was called VRChat
Matrices bless you prof.
If I had to do that instead of just row reducing with the identity matrix augmented I would've dropped linear algebra. 😭
The method used in this video for 3x3 matrices doesn't always work. Thanks.
ad-bc how do u get that ....I don't get it 🤦
That's the determinant of a 2x2 matrix; go back and watch Dave's previous video on evaluating determinants if you're stuck.
8:03 (1)(1) - (2)(0) = -1
8:05 oh shit