Question

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

Answer 1

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

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

Since A is a skew-symmetric matrix,
A = A^T

∴ `[(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)`