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Question
Find a matrix X such that 2A + B + X = O, where
If A = `[[8 0],[4 -2],[3 6]]` and B = `[[2 -2],[4 2],[-5 1]]`
, then find the matrix X of order 3 × 2 such that 2A + 3X = 5B.
Solution
2A+3X=5B
`⇒ 2[[8 0],[4 -2],[3 6]]+3x =5[[2 -2],[4 2],[-5 1]]`
`⇒[[16 0],[8 -4],[6 12]]+3x =[[10 -10],[20 10],[-25 5]]`
`⇒ 3x =[[10 -10],[20 10],[-25 5]]-[[16 0],[8 -4],[6 12]]`
`⇒ 3x = [[10 - 16 -10-0],[20-8 10+4],[-25 - 6 5-12]]`
`⇒ 3x= [[-6 -10],[12 14],[-31 -7]]`
`⇒= 1/3 [[-6 -10],[12 14],[-31 -7]]`
`∴⇒x = [[-2 (-10)/3],[12 14/3],[(-31)/3 (-7)/3]]`
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