# Solve the following : Find x, y, z if [2x531zy58] is a symmetric matrix. - Mathematics and Statistics

Sum

Solve the following :

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

#### Solution

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

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

Since A is a symmetric matrix,
A = AT

∴ [(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.

Concept: Algebra of Matrices
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