Question

Find a, b, c if `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` is a symmetric matrix.

Answer 1

Let A = `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` 

∴ A^T = `[(1, "b", -4),(3/5, -5, "c"),("a", -7, 0)]`

Since A is a symmetric matrix,

A = A^T

∴ `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)] = [(1, "b", -4),(3/5, -5, "c"),("a", -7, 0)]`

∴ By equality of matrices, we get

a = –4, b = `3/5`, c = –7