For the matrix A=left[begin{array}{ccc}2 & 0 | vedclass

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(B) To find the matrix of cofactors,we calculate the cofactor $A_{ij}$ for each element $a_{ij}$ using the formula $A_{ij} = (-1)^{i+j} M_{ij}$,where

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$\left[\begin{array}{ccc}0 & -8 & 4 \ -1 & 3 & -2 \ 1 & -7 & 2\end{array}ight]$

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(B) To find the matrix of cofactors,we calculate the cofactor $A_{ij}$ for each element $a_{ij}$ using the formula $A_{ij} = (-1)^{i+j} M_{ij}$,where $M_{ij}$ is the minor of the element $a_{ij}$.$A_{11} = (-1)^{1+1} \begin{vmatrix} 1 & 2 \ 1 & 2 \end{vmatrix} = (1)(2-2) = 0$$A_{12} = (-1)^{1+2} \begin{vmatrix} 3 & 2 \ -1 & 2 \end{vmatrix} = (-1)(6 - (-2)) = -8$$A_{13} = (-1)^{1+3} \begin{vmatrix} 3 & 1 \ -1 & 1 \end{vmatrix} = (1)(3 - (-1)) = 4$$A_{21} = (-1)^{2+1} \begin{vmatrix} 0 & -1 \ 1 & 2 \end{vmatrix} = (-1)(0 - (-1)) = -1$$A_{22} = (-1)^{2+2} \begin{vmatrix} 2 & -1 \ -1 & 2 \end{vmatrix} = (1)(4 - 1) = 3$$A_{23} = (-1)^{2+3} \begin{vmatrix} 2 & 0 \ -1 & 1 \end{vmatrix} = (-1)(2 - 0) = -2$$A_{31} = (-1)^{3+1} \begin{vmatrix} 0 & -1 \ 1 & 2 \end{vmatrix} = (1)(0 - (-1)) = 1$$A_{32} = (-1)^{3+2} \begin{vmatrix} 2 & -1 \ 3 & 2 \end{vmatrix} = (-1)(4 - (-3)) = -7$$A_{33} = (-1)^{3+3} \begin{vmatrix} 2 & 0 \ 3 & 1 \end{vmatrix} = (1)(2 - 0) = 2$Thus,the matrix of cofactors is $\left[\begin{array}{ccc}0 & -8 & 4 \ -1 & 3 & -2 \ 1 & -7 & 2\end{array}ight]$.

Element	Co-factor
$A$. $-1$	$(1)$ $-2$
$B$. $1$	$(2)$ $32$
$C$. $3$	$(3)$ $4$
$D$. $6$	$(4)$ $6$
	$(5)$ $-6$

For the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$,the matrix of cofactors is

Similar Questions

Match the following elements of the matrix $A = \left[\begin{array}{ccc} 1 & -1 & 0 \\ 0 & 4 & 2 \\ 3 & -4 & 6 \end{array}\right]$ with their co-factors and choose the correct answer.
Element Co-factor
$A$. $-1$ $(1)$ $-2$
$B$. $1$ $(2)$ $32$
$C$. $3$ $(3)$ $4$
$D$. $6$ $(4)$ $6$
$(5)$ $-6$

Find the minors and cofactors of the elements of the determinant $\left|\begin{array}{ccc}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{array}\right|$ and verify that $a_{11} A_{31}+a_{12} A_{32}+a_{13} A_{33}=0$.

The sum of the cofactors of the elements of the second row of the matrix $\begin{bmatrix} 1 & 3 & 2 \\ -2 & 0 & 1 \\ 5 & 2 & 1 \end{bmatrix}$ is

Find the minors and cofactors of the elements $a_{11}$ and $a_{21}$ in the determinant $\Delta = \begin{vmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{vmatrix}$.

If $A = \begin{bmatrix} x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1 \end{bmatrix}$,where $x$ and $y$ are non-zero real numbers,$\text{trace}(A) = 0$,and $\det(A) = -6$,then the minor of the element $1$ (at position $a_{13}$) of $A$ is:

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