Maharashtra State BoardHSC Commerce 12th Board Exam
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Find x, y, z if [0-5ixy0z32-20] is a skew symmetric matrix. - Mathematics and Statistics

Sum

Find x, y, z if `[(0, -5i, x),(y, 0, z),(3/2, - sqrt(2), 0)]` is a skew symmetric matrix.

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Solution

Let A = `[(0, -5i, x),(y, 0, z),(3/2, - sqrt(2), 0)]`

∴ AT = `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 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)]`

∴ By equality of matrices, we get

x = `(-3)/(2), y = 5"i", z = sqrt(2)`

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