Maharashtra State BoardHSC Commerce 12th Board Exam
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Find a, b, c, if abc[135ab-5-7-4c0] is a symmetric matrix. - Mathematics and Statistics

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Sum

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)]`

∴ 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.

Concept: Algebra of Matrices
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