If A = begin{bmatrix} 0 & 2 & 0 0 & 0 & 3 - | vedclass

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(B) To find the element in the $3^{rd}$ row and $3^{rd}$ column of the product matrix $AB$,we denote it as $C_{33}$.According to the rule of matrix mu

Vedclass · Accepted Answer

$4$

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(B) To find the element in the $3^{rd}$ row and $3^{rd}$ column of the product matrix $AB$,we denote it as $C_{33}$.According to the rule of matrix multiplication,$C_{33}$ is obtained by multiplying the elements of the $3^{rd}$ row of matrix $A$ with the corresponding elements of the $3^{rd}$ column of matrix $B$ and summing them up.$C_{33} = (A_{31} 	imes B_{13}) + (A_{32} 	imes B_{23}) + (A_{33} 	imes B_{33})$$C_{33} = (-2 	imes 3) + (2 	imes 5) + (0 	imes 0)$$C_{33} = -6 + 10 + 0$$C_{33} = 4$.Thus,the correct option is $B$.

If $A = \begin{bmatrix} 0 & 2 & 0 \\ 0 & 0 & 3 \\ -2 & 2 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 5 & -4 & 0 \end{bmatrix}$,then the element of the $3^{rd}$ row and $3^{rd}$ column in $AB$ will be:

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