If A = begin{bmatrix} 4 & x + 2 2x - 3 & x + | vedclass

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(B) matrix $A$ is symmetric if $A = A^T$,which implies that the element at the $i$-th row and $j$-th column is equal to the element at the $j$-th row

Vedclass · Accepted Answer

$5$

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(B) matrix $A$ is symmetric if $A = A^T$,which implies that the element at the $i$-th row and $j$-th column is equal to the element at the $j$-th row and $i$-th column,i.e.,$a_{ij} = a_{ji}$.For the given matrix $A = \begin{bmatrix} 4 & x + 2 \ 2x - 3 & x + 1 \end{bmatrix}$,we have $a_{12} = x + 2$ and $a_{21} = 2x - 3$.Since the matrix is symmetric,we set $a_{12} = a_{21}$:$x + 2 = 2x - 3$Subtracting $x$ from both sides,we get $2 = x - 3$.Adding $3$ to both sides,we get $x = 5$.Therefore,the correct option is $B$.

If $A = \begin{bmatrix} 4 & x + 2 \\ 2x - 3 & x + 1 \end{bmatrix}$ is a symmetric matrix,then $x = $

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