Question

if A =[5 x+2 / 4x-7 x-2] is a symmetric matrix, then x is​

Answer 1

Given :    $A=\left[\begin{array}{ccc}5&x+2\\4x-7 &x-2\end{array}\right]$

A  is a symmetric matrix

To Find :  Value of x

Solution:

A symmetric matrix is a square matrix that is equal to its transpose

in Transpose matrix Rows and column are interchanged

$A=\left[\begin{array}{ccc}5&x+2\\4x-7 &x-2\end{array}\right]$

$A^T=\left[\begin{array}{ccc}5&4x-7\\x+2 &x-2\end{array}\right]$

$A=A^T$

$\left[\begin{array}{ccc}5&x+2\\4x-7 &x-2\end{array}\right] = \left[\begin{array}{ccc}5&4x-7\\x+2 &x-2\end{array}\right]$

x + 2 = 4x - 7

=> 3x = 9

=> x = 3

Value of x = 3

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