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प्रश्न
Find non-zero values of x satisfying the matrix equation:
`x[(2x, 2),(3, x)] + 2[(8, 5x),(4, 4x)] = 2[(x^2 + 8, 24),(10, 6x)]`
उत्तर
The given equation can be written as
`[(2x^2, 2x),(3x, x^2)] + [(16, 10x),(8, 8x)] = [((2x^2 + 16), 18),(20, 12x)]`
⇒ `[(2x^2 + 16, 12x),(3x + 8, x^2 + 8x)] = [(2x^2 + 16, 48),(20, 12x)]`
Equating the corresponding elements we get
12x = 48
3x + 8 = 20
x2 + 8x = 12x
∴ x = `48/12` = 4
3x = 20 – 8 = 12
⇒ x2 = 12x – 8x = 4x
⇒ x2 – 4x = 0
x = 0, x = 4
∴ x = 4
Hence, the non-zero values of x is 4.
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