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Question
Find a, b, c, if `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` is a symmetric matrix.
Solution
Let A = `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]`
∴ AT = `[(1, "b" , -4),(3/5, -5, "c"),("a", -7, 0)]`
Since A is a symmetric matrix,
A = AT
∴ `[(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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