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Question
If the matrix `[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`, is a skew symmetric matrix, find the values of a, b and c.
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Solution
Let A = `[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`
A = `[(0, 2, "c"),("a", "b", 1),(3, -1, 0)]`
For skew symmetric matrix, A' = – A.
⇒ `[(0, 2, "c"),("a", "b", 1),(3, -1, 0)] = -[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`
⇒ `[(0, 2, "c"),("a", "b", 1),(3, -1, 0)] = [(0, -"a", -3),(-2, -"b", 1),(-"c", -1, 0)]`
Equating the corresponding elements, we get
a = – 2, b = – b
⇒ 2b = 0
⇒ b = 0
And c = – 3
Hence, a = – 2, b = 0 and c = – 3.
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