If A = \(\left[ \begin{matrix} 2 & x-3 & x-2 \\ 3 & -2 & -1 \\ 4 & -1 & -5 \\ \end{matrix} \right]\) is a symmetric matrix then x

Question

Question

Answer 1

Concept:

Symmetric Matrix:

Square matrix A is said to be symmetric if the transpose of matrix A is equal to matrix A itself
A^T = A or A’ = A

Where, A^T or A’ denotes the transpose of matrix

Where a_ij and a_ji is an element present in matrix.

Calculation:

Given:

A is a symmetric matrix,

⇒ A^T = A or a_ij = a_ji

A = \(\left[ \begin{matrix} 2 & x-3 & x-2 \\ 3 & -2 & -1 \\ 4 & -1 & -5 \\ \end{matrix} \right]\)

So, by property of symmetric matrices

⇒ a₁₂ = a₂₁

⇒ x – 3 = 3

∴ x = 6