Question

If `2[(3, x),(0, 1)] + 3[(1, 3),(y, 2)] = [(z, -7),(15, 8)]`, the values of x, y and z are ______.

विकल्प

• x = 8, y = – 5 and z = 9

• x = – 8, y = 5 and z = 9

• x = – 8, y = – 5 and z = – 9

• x = – 8, y = 5 and z = – 9

Answer 1

If `2[(3, x),(0, 1)] + 3[(1, 3),(y, 2)] = [(z, -7),(15, 8)]`, the values of x, y and z are x = – 8, y = 5 and z = 9.

Explanation:

Given

`2[(3, x),(0, 1)] + 3[(1, 3),(y, 2)] = [(z, -7),(15, 8)]`

`\implies [(6, 2x),(0, 2)] + [(3, 9),(3y, 6)] = [(z, -7),(15, 8)]`

`\implies [(6 + 3, 2x + 9),(3y, 2 + 6)] = [(z, -7),(15, 8)]`

`\implies [(9, 2x + 9),(3y, 8)] = [(z, -7),(15, 8)]`

Thus their corresponding entries are equal.

∴ 9 = z; 2x + 9 = – 7

`\implies` 2x = – 7 – 9 = – 16

`\implies` x = – 8

And 3y = 15 `\implies` y = 5