Match the following elements of the matrix A | vedclass

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(C) Let $A = \left[\begin{array}{ccc} 1 & -1 & 0 \ 0 & 4 & 2 \ 3 & -4 & 6 \end{array}ight]$.The cofactor $C_{ij}$ of an element $a_{ij}$ is given

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$A-4, B-2, C-1, D-3$

Vedclass · Answer

(C) Let $A = \left[\begin{array}{ccc} 1 & -1 & 0 \ 0 & 4 & 2 \ 3 & -4 & 6 \end{array}ight]$.The cofactor $C_{ij}$ of an element $a_{ij}$ is given by $(-1)^{i+j} M_{ij}$, where $M_{ij}$ is the minor.$1$. For element $-1$ at position $(1, 2)$: $C_{12} = (-1)^{1+2} \left|\begin{array}{cc} 0 & 2 \ 3 & 6 \end{array}ight| = -1(0 - 6) = 6$. So, $A-4$.$2$. For element $1$ at position $(1, 1)$: $C_{11} = (-1)^{1+1} \left|\begin{array}{cc} 4 & 2 \ -4 & 6 \end{array}ight| = 1(24 - (-8)) = 32$. So, $B-2$.$3$. For element $3$ at position $(3, 1)$: $C_{31} = (-1)^{3+1} \left|\begin{array}{cc} -1 & 0 \ 4 & 2 \end{array}ight| = 1(-2 - 0) = -2$. So, $C-1$.$4$. For element $6$ at position $(3, 3)$: $C_{33} = (-1)^{3+3} \left|\begin{array}{cc} 1 & -1 \ 0 & 4 \end{array}ight| = 1(4 - 0) = 4$. So, $D-3$.Thus, the matching is $A-4, B-2, C-1, D-3$.Therefore, option $C$ is correct.

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

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

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