Question

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

Options

• `[(-3, -3, 5),(3, 4, 2)]`

• `[(3, 3, 5),(-3, -4, -2)]`

• `[(3, 3, -5),(-3, -4, -2)]`

• `[(-3, -3, -5),(3, 4, 2)]`

Answer 1

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

Explanation:

Given:

A = `[(0, -3, 4),(1, 0, 2)]`

B = `[(0, -3, 4),(1, 0, 2)]`

A + B + C = 0

so, C = − (A + B)

Step 1: Sum A + B

A + B = `[(0, -3, 4),(1, 0, 2)]` + `[(0, -3, 4),(1, 0, 2)]`

= `[(0 + (-3), -3 + 0, 4 + 1),(1 + 2, 0 + 4, 2 + 0)]`

= `[(-3, -3, 5),(3, 4, 2)]`

Step 2: Find C = − (A + B)

C = `- [(-3, -3, 5),(3, 4, 2)]`

= `[(-(-3), -(-3), -(5)),(- (3), -(4), -(2))]`

= `[(3, 3, -5),(-3, -4, -2)]`