In the matrix begin{bmatrix} -1 & x & 3 -4 & | vedclass

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(C) Let $A = \begin{bmatrix} -1 & x & 3 \ -4 & -5 & -6 \ -7 & y & 9 \end{bmatrix}$.The cofactor of the element at position $(2, 3)$ (which is $-6$)

Vedclass · Accepted Answer

$-2$

Vedclass · Answer

(C) Let $A = \begin{bmatrix} -1 & x & 3 \ -4 & -5 & -6 \ -7 & y & 9 \end{bmatrix}$.The cofactor of the element at position $(2, 3)$ (which is $-6$) is given by $C_{23} = (-1)^{2+3} \begin{vmatrix} -1 & x \ -7 & y \end{vmatrix} = -1(-y - (-7x)) = -1(-y + 7x) = y - 7x$.Given $C_{23} = 22$, we have $y - 7x = 22$  --- $(1)$.The cofactor of the element at position $(3, 1)$ (which is $-7$) is given by $C_{31} = (-1)^{3+1} \begin{vmatrix} x & 3 \ -5 & -6 \end{vmatrix} = 1(-6x - (-15)) = -6x + 15$.Given $C_{31} = 27$, we have $-6x + 15 = 27$.$-6x = 12 \implies x = -2$.Substitute $x = -2$ into equation $(1)$:$y - 7(-2) = 22$$y + 14 = 22 \implies y = 8$.Now, calculate $5x + y$:$5(-2) + 8 = -10 + 8 = -2$.

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

In the matrix $\begin{bmatrix} -1 & x & 3 \\ -4 & -5 & -6 \\ -7 & y & 9 \end{bmatrix}$, if the cofactors of $-6$ and $-7$ are respectively $22$ and $27$, then $5x + y = $

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