Clarence
  • Clarence
I don't understand this question. Calculate the second term in the cofactor expansion along the third row for the matrix: [[-1,-1,-1,-1],[-1,1,2,0],[1,-1,0,2],[-1,-1,-1,-1]]
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Clarence
  • Clarence
\[\left[\begin{matrix}-1 & -1 & -1 & -1 \\ -1 & 1 & 2 & 0 \\ 1 & -1 & 0 & 2 \\ -1 & -1 & -1 & -1\end{matrix}\right]\]
Clarence
  • Clarence
So the third row would be [1, -1, 0, 2]
Clarence
  • Clarence
Second term being -1

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Clarence
  • Clarence
So do I just use -1 times the rest of the matrix?
ganeshie8
  • ganeshie8
\[\left[\begin{matrix}-1 & -1 & -1 & -1 \\ -1 & 1 & 2 & 0 \\ 1 & \color{red}{-1} & 0 & 2 \\ -1 & -1 & -1 & -1\end{matrix}\right]\]
anonymous
  • anonymous
I guess you can take the determinant?
anonymous
  • anonymous
Then multiply by -1
Clarence
  • Clarence
Take the determinant of the original matrix and times that by -1?
ganeshie8
  • ganeshie8
whats the definition of "term" that your professor uses ?
ganeshie8
  • ganeshie8
does the determinant has \(4!=24\) terms or just \(4\) terms according to your prof ?
Clarence
  • Clarence
I think she'd say that that'd be just 4 terms.
ganeshie8
  • ganeshie8
** then, you just need to find the cofactor of -1, which is at 3,2 location, then multiply that by -1
ganeshie8
  • ganeshie8
** cofactor of \(A_{32}\)= \((-1)^{3+2}\begin{vmatrix}-1&-1&-1\\-1&2&0\\-1&-1&-1\end{vmatrix}\)
Clarence
  • Clarence
Okay, I am obviously not understanding this question because the answer I got was 0...
ganeshie8
  • ganeshie8
Right, I think your prof wants the first term out of those 24 terms in the determinant
Clarence
  • Clarence
There's a similar question on this website that went unanswered:http://openstudy.com/study#/updates/5039e2afe4b043c156a3277c
Clarence
  • Clarence
How did they obtain -20 in this example? https://au.answers.yahoo.com/question/index?qid=20120826032029AANjdNA
ganeshie8
  • ganeshie8
the answer is either 0 or 2 0 if you consider 4 terms in the determinant 2 if you consider 24 terms
ganeshie8
  • ganeshie8
yahoo answers is not that reliable..
Clarence
  • Clarence
Aha, I know, I was just trying to work out how they managed to get -20 that's all
ganeshie8
  • ganeshie8
they got -40 right ?
Clarence
  • Clarence
Yeah.
ganeshie8
  • ganeshie8
remember how to find cofactor of a term ?
Clarence
  • Clarence
Yes, but it's a bit hard to write it all on here.
ganeshie8
  • ganeshie8
[3,-1,2,-1] [-2,2,1,2] [2,-2,2,1] [-1,3,2,-1] to find the cofactor of -2 at position 3,2 you simply find the determinant of the small matrix obtained by deleting 3rd row and second column, then fix the sign
ganeshie8
  • ganeshie8
removing 3rd row and 2nd column, [3,2,-1] [-2,1,2] [-1,2,-1]
Clarence
  • Clarence
And then multiplying all that by -2.
Clarence
  • Clarence
What I don't understand is how they ended up getting (-2) x (-20) to get 40.
ganeshie8
  • ganeshie8
before that, multiply the determinant by \((-1)^{3+2}\) to get the cofactor
ganeshie8
  • ganeshie8
what do you get for determinant of [3,2,-1] [-2,1,2] [-1,2,-1]
Clarence
  • Clarence
Ohh... My bad..
Clarence
  • Clarence
So for my particular question, the determinant of the submatrix is just 0, does this mean that the answer is just 0 then?
ganeshie8
  • ganeshie8
let me just quote my previous reply ``` the answer is either 0 or 2 0 if you consider 4 terms in the determinant 2 if you consider 24 terms ```
Clarence
  • Clarence
Yeah, I remember reading that, I was just confused as to how you managed to get 2 as well if I considered 24 terms rather than 4
ganeshie8
  • ganeshie8
lets work it step by step
ganeshie8
  • ganeshie8
how many terms are there in the determinant of a 2x2 matrix ?
ganeshie8
  • ganeshie8
\[ \begin{vmatrix}a&b\\c&d\\\end{vmatrix} = ad-bc\] two terms, right ?
Clarence
  • Clarence
Yes.
ganeshie8
  • ganeshie8
how about the determinant of a \(3\times 3\) matrix, how many terms ?

Looking for something else?

Not the answer you are looking for? Search for more explanations.