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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 ______.
Options
`[(-7, 5),(6, -2)]`
`[(-7, -5),(-6, 2)]`
`[(-7, 5),(6, 2)]`
`[(7, 5),(-6, 2)]`
MCQ
Fill in the Blanks
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Solution
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)]`
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