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प्रश्न
For what value of x, the matrix A = `[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)]` is skew – symmetric
उत्तर
A = `[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)]`
AT = `[(0, -1, 2),(1, 0, -3),(-2, x^3, 0)]`
The matrix A is skew-symmetric if A = – AT
`[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)] = - [(0, -1, 2),(1, 0, -3),(-2, x^3, 0)]`
`[(0, 1, -2),(-1, 0, x^3),(2, -3, 0)] + [(0, -1, 2),(1, 0, -3),(-2, x^3, 0)] = [(0, 0, 0),(0, 0, 0),(0, 0, 0)]`
`[(0 + 0, 1 - 1, -2 + 2),(-1 + 1, 0 + 0, x^3 - 3),(2 - 2, -3 x^3, 0 + 0)] = [(0, 0, 0),(0, 0, 0),(0, 0, 0)]`
`[(0, 0, 0),(0, 0, x^3 - 3),(0, x^3 - 3, 0)] = [(0, 0, 0),(0, 0, 0),(0, 0, 0)]`
Equating the corresponding entries
x3 – 3 = 0
x3 = 3
⇒ x = `3^(1/3)`
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