Question

Would someone clarify if there's an error here? Example 2.2 located at: http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-b-matrices-and-systems-of-equations/session-11-matrix-inverses/MIT18_02SC_MNotes_m2.pdf

Shouldn't the cofactor matrix be (1 -1 -1
0 0 0
-1 1 1)

Would someone explain how the cofactor matrix presented in the pdf was derived? Thanks.

Answer 1

cofactor, there is a +-+- alternating grid and sub determinants

Answer 2

if memory serves that is

Answer 3

Yeah, but the cofactor I derived is different to the one there. Is it the same for you?

Answer 4

\[\begin{pmatrix}
+\begin{vmatrix}1&1\\0&1 \end{vmatrix}&
-\begin{vmatrix}0&1\\1&1 \end{vmatrix}
&+\begin{vmatrix}0&1\\1&0 \end{vmatrix}\\

-\begin{vmatrix}0&-1\\0&1 \end{vmatrix}&
+\begin{vmatrix}1&-1\\1&1 \end{vmatrix}&
-\begin{vmatrix}1&0\\1&0 \end{vmatrix}&\\

+\begin{vmatrix}0&-1\\1&1 \end{vmatrix}&
-\begin{vmatrix}1&-1\\0&1 \end{vmatrix}&
+\begin{vmatrix}1&0\\0&1 \end{vmatrix}&\\

\end{pmatrix}\]

Answer 5

1 --1 -1
-0 1--1 0
--1 -1 1


1 1 -1
0 2 0
1 -1 1

works fine for me

Answer 6

tell me how you got your subdeterminants, that tends to be the confusing part of it all

Answer 7

otherwise, its just keep track of the calculations ... theres alot of error room in this thing

Answer 8

Ahh I see now, you're right I made a mistake, thank you.

Answer 9

yep