Question

Solve the following :

Find x, y, z if `[(2, x, 5),(3, 1, z),(y, 5, 8)]` is a symmetric matrix.

Answer 1

Let A = `[(2, x, 5),(3, 1, z),(y, 5, 8)]`

∴ A^T = `[(2, 3, y),(x, 1, 5),(5, z, 8)]`

Since A is a symmetric matrix,
A = A^T

∴ `[(2, x, 5),(3, 1, z),(y, 5, 8)] = [(2, 3, y),(x, 1, 5),(5, z, 8)]`

∴ By equality of matrices, we get
x = 3, y = 5, z = 5.