If you're reading this, there may be some confusion on the signs "alternating". Just putting this out there if anyone needs it. The way it works: + - + - + - + - + For some reason most books / videos choose just the positive ones to explain. Using Row 2 as example (from the video), you get: 24 - 60 + 36 = 0 :) Good Luck!
Another way is if you add the row and column number together. If its even its + if its odd its -. Example row 3 column 1, 3+1=4 even so its +. Hope this helps
In case the visual method for determining the alternating sign of the co-efficient is confusing, another way to determine the sign is (-1) ^ row + column. For example, F would be (-1) ^ 2 + 3 = -1 ^ 5 = -1.
hahaha don't be too hard on yourself =). If you're looking for some more info on matrices check out videos 35-44 here: engineer4free.com/linear-algebra
You start with a positive value for the row or column then alternate. So finding the determinant via cofactors expansion of row 2 would be d|...| - e|...| +f|...|
because the -/+ of the elements comes down the -1^i+,. so with B it is in row 1and column 2, so i+j=3. and because of this, -1^i+j, here is -1^3, which is -1 :)
![[Linear Algebra] Cofactor Expansion](http://i.ytimg.com/vi/ZAECu1mkFY8/mqdefault.jpg)
![[Linear Algebra] Cofactor Expansion](/img/tr.png)
This 7 minute video finally made me understand a concept gone over a 50 minute lecture, and 2 hours of struggling to undertsnad a textbook. Thank you.
Yeah man simple, easy to understand explanation! great work, thanks.
Thanks Junaid!!
The best tutorial on linear algebra I found on YT so far. Much appreciated!
If you're reading this, there may be some confusion on the signs "alternating".
Just putting this out there if anyone needs it.
The way it works:
+ - +
- + -
+ - +
For some reason most books / videos choose just the positive ones to explain.
Using Row 2 as example (from the video), you get: 24 - 60 + 36 = 0
:) Good Luck!
Thanks, I was wondering about that.
Another way is if you add the row and column number together. If its even its + if its odd its -. Example row 3 column 1, 3+1=4 even so its +.
Hope this helps
So wouldn't it be -24 + 60 - 36?
In case the visual method for determining the alternating sign of the co-efficient is confusing, another way to determine the sign is (-1) ^ row + column. For example, F would be (-1) ^ 2 + 3 = -1 ^ 5 = -1.
Took me a few hours but with help of this video it finally makes sense now
Thank you for this. I'm finding it easy to recap on matrices now.
I'm so happy I found your channel!
Me too!!! =)
i'm pretty stupid but I understood this :D Thank you!
hahaha don't be too hard on yourself =). If you're looking for some more info on matrices check out videos 35-44 here: engineer4free.com/linear-algebra
This video is very concise and easy to understand. Thank you for making this!
Glad it was helpful!! The full playlist is here: ruclips.net/p/PL2C8B5877FC12E315
Thank you
Good stuff. Thank you
At 0:40 you said it always alternates + - + but if I take row 2 isn't it -d| | +e| | -f| |?
You start with a positive value for the row or column then alternate. So finding the determinant via cofactors expansion of row 2 would be d|...| - e|...| +f|...|
@@Engineer4Free no its -d +e -f ... the formula is ((-1)^i+j) * M(...)
@@Saronite you're right
@@Engineer4Free No, it's -, +, -
I love your voice! And great explanation ^^
Thanks Tokki!! ^_^
Very helpful! Thanks
Glad it was helpful!! =) The full playlist is here too: engineer4free.com/linear-algebra
Great 👍🏻 thank you 🌹
You’re welcome 😊
This was very helpful. Thank you!!
Glad to hear it Claudia and thanks for letting me know!
Thank youuu
You’re welcome!!!
If I use the second column, I get the same determinant as if I use the first row, except multiplied by -1.
damn bro thanks for the explanation, i was pretty confused here but thank you for clearing my doubts :)
where is the cofactor expansion stated on the caption of the video!
Dont use simple terms use some negative as well 😢
Why there is a negative sign in b and f?
because the -/+ of the elements comes down the -1^i+,. so with B it is in row 1and column 2, so i+j=3. and because of this, -1^i+j, here is -1^3, which is -1 :)
wow how do you write that fast
Bro 7 minute equal my lecture 50 minute
I don't see you determine a coefactor matrix what-so-ever....
You did not explain the cofactor at all