Let A = [a_{ij}] = begin{bmatrix} log_5 128 & | vedclass

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(C) Given $A = \begin{bmatrix} \log_5 128 & \log_4 5 \ \log_5 8 & \log_4 25 \end{bmatrix} = \begin{bmatrix} 7 \log_5 2 & \frac{1}{2} \log_2 5 \ 3 \l

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$242$

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(C) Given $A = \begin{bmatrix} \log_5 128 & \log_4 5 \ \log_5 8 & \log_4 25 \end{bmatrix} = \begin{bmatrix} 7 \log_5 2 & \frac{1}{2} \log_2 5 \ 3 \log_5 2 & \log_2 5 \end{bmatrix}$.First,calculate the determinant $|A|$:$|A| = (7 \log_5 2)(\log_2 5) - (3 \log_5 2)(\frac{1}{2} \log_2 5) = 7 - \frac{3}{2} = \frac{11}{2}$.The matrix $C$ is defined by $C_{ij} = \sum_{k=1}^2 a_{ik} A_{jk}$.For $i=j$,$C_{ii} = \sum_{k=1}^2 a_{ik} A_{ik} = |A| = \frac{11}{2}$.For $i 
eq j$,$C_{ij} = \sum_{k=1}^2 a_{ik} A_{jk} = 0$ (property of determinants).Thus,$C = \begin{bmatrix} |A| & 0 \ 0 & |A| \end{bmatrix} = \begin{bmatrix} 11/2 & 0 \ 0 & 11/2 \end{bmatrix}$.The determinant $|C| = (11/2) 	imes (11/2) = 121/4$.Therefore,$8|C| = 8 	imes (121/4) = 2 	imes 121 = 242$.

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

Let $A = [a_{ij}] = \begin{bmatrix} \log_5 128 & \log_4 5 \\ \log_5 8 & \log_4 25 \end{bmatrix}$. If $A_{ij}$ is the cofactor of $a_{ij}$,$C_{ij} = \sum_{k=1}^2 a_{ik} A_{jk}$,$1 \leq i, j \leq 2$,and $C = [C_{ij}]$,then $8|C|$ is equal to:

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

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Write the minors and cofactors of the elements of the following determinant: $\left|\begin{array}{ccc}1 & 0 & 4 \\ 3 & 5 & -1 \\ 0 & 1 & 2\end{array}\right|$

Let $A = [a_{ij}]_{n \times n}$ be a square matrix and let $c_{ij}$ be the cofactor of $a_{ij}$ in $A$. If $C = [c_{ij}]$,then which of the following is true?

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