1. Tardigrade
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  4. If the matrix A = [5&2&x y&2&-3 4&t&-7] is a symmetric matrix, then find the value of x, y and t respectively,

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Q. If the matrix $A = \begin{bmatrix}5&2&x\\ y&2&-3\\ 4&t&-7\end{bmatrix}$ is a symmetric matrix, then find the value of $x, y$ and $t$ respectively,

Matrices

Solution:

$A$ is a symmetric matrix $\therefore A = A^T $
$ \Rightarrow \begin{bmatrix}5&2&x\\ y&2&-3\\ 4&t&-7\end{bmatrix} = \begin{bmatrix}5&y&4\\ 2&2&t\\ x&-3&-7\end{bmatrix}$
On comparing, we get
$\Rightarrow y=2, x = 4, t = -3$