Question

If A = `[(2, -1),(2, 0)], B = [(-3, 2),(4, 0)], C = [(1, 0),(0, 2)]` and A + D= 2B + C, then matrix D is ______.

विकल्प

• `[(-7, 5),(6, -2)]`

• `[(-7, -5),(-6, 2)]`

• `[(-7, 5),(6, 2)]`

• `[(7, 5),(-6, 2)]`

Answer 1

If A = `[(2, -1),(2, 0)], B = [(-3, 2),(4, 0)], C = [(1, 0),(0, 2)]` and A + D= 2B + C, then matrix D is `underlinebb([(-7, 5),(6, 2)])`.

Explanation:

A + D = 2B + C

2B = `2 xx [(-3, 2),(4, 0)]`

= `[(-6, 4),(8, 0)]`

2B + C = `[(-6, 4),(8, 0)] + [(1, 0),(0, 2)]`

= `[(-5, 4),(8, 2)]`

So,

A + D = `[(-5, 4),(8, 2)]`

Use D = (2B + C) − A

D = `[(-5, 4),(8, 2)] - [(2, -1),(2, 0)]`

= `[(-5 - 2, 4 - (-1)),(8 - 2, 2 - 0)]`

= `[(-7, 5),(6, 2)]`