The co-factors of the elements of the second | vedclass

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Question

(A) Let the matrix be $A = \begin{bmatrix} 1 & -1 & 2 \ 3 & 2 & 1 \ -1 & 3 & 4 \end{bmatrix}$.The elements of the second column are $a_{12} = -1$,$a

Vedclass · Accepted Answer

$-13, 6, 5$

Vedclass · Answer

(A) Let the matrix be $A = \begin{bmatrix} 1 & -1 & 2 \ 3 & 2 & 1 \ -1 & 3 & 4 \end{bmatrix}$.The elements of the second column are $a_{12} = -1$,$a_{22} = 2$,and $a_{32} = 3$.The co-factor $A_{ij}$ is given by $(-1)^{i+j} M_{ij}$,where $M_{ij}$ is the minor of the element $a_{ij}$.For $A_{12}$: $A_{12} = (-1)^{1+2} \begin{vmatrix} 3 & 1 \ -1 & 4 \end{vmatrix} = -(12 - (-1)) = -(13) = -13$.For $A_{22}$: $A_{22} = (-1)^{2+2} \begin{vmatrix} 1 & 2 \ -1 & 4 \end{vmatrix} = +(4 - (-2)) = +(6) = 6$.For $A_{32}$: $A_{32} = (-1)^{3+2} \begin{vmatrix} 1 & 2 \ 3 & 1 \end{vmatrix} = -(1 - 6) = -(-5) = 5$.Thus,the co-factors are $-13, 6, 5$.

The co-factors of the elements of the second column of $\begin{bmatrix} 1 & -1 & 2 \\ 3 & 2 & 1 \\ -1 & 3 & 4 \end{bmatrix}$ are:

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