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Question
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.
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