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Question
Find x, y, z if `[(0, -5i, x),(y, 0, z),(3/2, - sqrt(2), 0)]` is a skew symmetric matrix.
Solution
Let A = `[(0, -5i, x),(y, 0, z),(3/2, - sqrt(2), 0)]`
∴ AT = `[(0, y, (3)/(2)),(-5"i", 0, -sqrt(2)),(x, z, 0)]`
Since A is a skew-symmetric matrix,
A = AT
∴ `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)] = [(0, y, (3)/(2)),(-5"i", 0, -sqrt(2)),(x, z, 0)]`
∴ `[(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", z = sqrt(2)`
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