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

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#### Solution

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.

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