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Question
Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.
Solution
Let A = `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]`
∴ A' = `[(0, y, 3/2),(-5"i", 0, -sqrt(2)),(x, z, 0)]`
∴ –A' = `-[(0, y, 3/2),(-5"i", 0, -sqrt(2)),(x, z, 0)]`
= `[(0, -y, -3/2),(5"i", 0, sqrt(2)),(-x, -z, 0)]`
Since A is a skew-symmetric matrix, A = – A'
∴ `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)] = [(0, -y, -3/2),(5"i", 0, sqrt(2)),(-x, -z, 0)]`
∴ by equality of matrices, we get,
x = `-3/2, y = 5"i" and z = sqrt(2)`
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