Question

If 2 `[(x, 7),(9, y - 5)] + [(6, -7),(4, 5)] = [(10, 7),(22, 15)]`, then the value of x is ______.

Options

• 1

• 2

• 3

• 4

Answer 1

If 2 `[(x, 7),(9, y - 5)] + [(6, -7),(4, 5)] = [(10, 7),(22, 15)]`, then the value of x is 2.

Explanation:

`2 xx [(x, 7),(9, y - 5)] + [(6, -7),(4, 5)] = [(10, 7),(22, 15)]`

Multiply the first matrix by 2

`2 xx [(x, 7),(9, y - 5)]`

= `[(2x, 14),(18, 2(y - 5))]`

Add the second matrix

`[(2x, 14),(18, 2(y - 5))] + [(6, -7),(4, 5)]`

= `[(2x + 6, 14 - 7),(18 + 4, 2(y - 5) + 5)]`

= `[(2x + 6, 7),(22, 2y - 10 + 5)]`

= `[(2x + 6, 7),(22, 2y - 5)]`

Set equal to the RHS

`[(2x + 6, 7),(22, 2y - 5)] = [(10, 7),(22, 15)]`

Now compare corresponding elements:

2x + 6 = 10

2x = 10 − 6

2x = 4

x = `4/2`

x = 2