Question

If X + Y = `[(3, 0),(1, 5)]` and X − Y = `[(5, 0),(9, 5)]` then matrix Y is ______.

Options

• `[(-1, 0),(-4, 0)]`

• `[(-1, 0),(4, 0)]`

• `[(1, 0),(-4, 0)]`

• [(1, 0),(4, 0)]

Answer 1

If X + Y = `[(3, 0),(1, 5)]` and X − Y = `[(5, 0),(9, 5)]` then matrix Y is `underlinebb([(-1, 0),(-4, 0)])`.

Explanation:

We are given two matrix equations:

X + Y = `[(3, 0),(1, 5)]`   ...(1)

X − Y = `[(5, 0),(9, 5)]`   ...(2)

(X + Y) + (X − Y) = `[(3, 0),(1, 5)] + [(5, 0),(9, 5)]`

⇒ 2X = `[(8, 0),(10, 10)]`

⇒ X = `[(4, 0),(5, 5)]`

Substitute X into equation (1) to find Y

X + Y = `[(3, 0),(1, 5)]`

⇒ `[(4, 0),(5, 5)]  + Y = [(3, 0),(1, 5)]`

⇒ Y = `[(3, 0),(1, 5)] - [(4, 0),(5, 5)]`

⇒ Y = `[(-1, 0),(-4, 0)]`