If the matrix `A=[5 2x y z-3 4t-7]` is a symmetric matrix, find `x ,\ y ,\ z` and `t` .

Explanation

`A= [[5,2,x],[y,z,-3],[4,t,-7]]`

`Rightarrow A^T = [[5,y,4],[2,z,t],[x,-3,-7]]`

Since, `A` is symmetric matrix. So, `(A^T) = A`

`Rightarrow [[5,y,4],[2,z,t],[x,-3,-7]] = [[5,2,x],[y,z,-3],[4,t,-7]]`

The corresponding elements of two equal matrices are equal.

So we get,

`Rightarrow x=4`

`Rightarrow y=2`

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