Question

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)]`

Answer 1

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.