How to solve this A-Level matrix problem!
HTML-код
- Опубликовано: 1 июн 2024
- A-Level Further Maths Question: Given a 3 by 3 matrix, show that this matrix is non-singular and find the inverse of this matrix. This question is from the A-Level maths exam qualifications.pearson.com/co....
You can see my original video: • First time solving an ...
Shop my math t-shirts & hoodies on Amazon: 👉 amzn.to/3qBeuw6
-----------------------------
I help students master the basics of math. You can show your support and help me create even better content by becoming a patron on Patreon 👉 / blackpenredpen . Every bit of support means the world to me and motivates me to keep bringing you the best math lessons! Thank you!
-----------------------------
#math #algebra #mathbasics
Love how you are so eager to fix your mistakes. Great video btw.
I almost had a heart attack when you forgot to transpose in the wrong version. 😅Thank you for fixing it. ❤
whoaaaawww!!! wish i knew this trick before... will have saved so much time during my F3 (A-level) exam.
but np, got full marks hehe
It's brave to admit that sometimes you could go wrong in A level maths. Love your channel keep going man🎉
The way I learned to find the inverse of a square matrix is to augment the square matrix with an identity matrix, then use matrix row reduction to drive the original matrix to identity. The augmentation is now the inverse.
That's the regular way to find the inverse. It's called the Gauss-Jordan method. The trick showed in the video is based on Cramer's rule.
Matrix are pretty cool to learn. The Matrix rule for when you see two equations stacked on top on each other. A while ago I learn the Cramer rule. I should review the Cramer rule. I wish I new it back in high school in freshman year because that would have same me a lot of time instead of using Elimination rule.
Cramer's rule is almost always slower than Gaussian elimination in practice, especially for extremely large matrices. The only reason it is taught is because it offers a way to solve matrices algebraically, and not just algorithmically.
Are you familiar with the Bareiss algorithm for determinants? It's not much use for hand-calculating 3x3 matrices; but if you have to do a computer program and larger matrices, it's a life-saver. It's roughly as fast as Gaussian elimination, but it doesn't introduce division inaccuracies all over the place. And it's crazy simple to program.
When you copy down the top two rows, copy the full expanded row, all five elements. That way you don’t have to remember which 2x2 section to copy.
I would love to see a video where you proof this formula, could you do it please?🥺🤩 It’d be really helpful
This is a math channel. You really should attempt to prove it yourself. It is very easy to do. It's just the method of cofactors with the numbers rearranged a bit to make the working easier.
Replace the elements of the matrix with general elements a, b, c, … h, i.
Then find the inverse using this method. To prove just multiply and show the results is the identity matrix.
So to start:
a b c a b
d e f d e
g h i g h
a b c a b
d e f d e
Then ignore row 1 and column 1 and use the determinants of the 2x2 matrices.
ei-fh fg-di dh-eg
Etc
I would try to show the whole proof, but spell check changes almost every pair of letters I enter. 😢
My friends has CP2 tomorrow so good luck to them
Your A level questions give me PTSD … I did super well on the S paper but it left my brain mushed.
bprp, where do you get your markers, i know they are expo. but i want to know where you get them from because i have been searching and i cant find those types, i just need them because all my markers run out within a week or so ❤🙏🙏
I got them on Amazon: www.amazon.com/dp/B00006IFIN/ref=cm_sw_r_as_gl_api_gl_i_RCZNQZ8RJ9GEYTWFM4KY?linkCode=ml2&tag=blackpenredpe-20
@@bprpmathbasics thanks
Can you please do aqa A level Further Maths Mechanics papers!! My pure maths is okay but my mechanics is terrible!!! Please help me
pls make a video on this problem. if a = 7-4*sqrt 3, find sqrt(a) + 1/sqrt(a)
That's just basic rationalisation.
Yo i understood that 28≠0
so early here
bprp math basics, You're awesome! Let's be friends, okay?
wanna play blox fruits