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Question
If A = `[[2 -2],[4 2],[-5 1]],B=[[8 0],[4 -2],[3 6]]`
, find matrix X such that 2A + 3X = 5B.
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Solution
Given: 2A+3X=5B
`⇒ 2 [[2 -2],[4 2],[-5 1]]+3X =5[[8 0],[4 -2],[3 6]]`
`⇒ [[4 -4],[8 4],[-10 2]]+3X=[[40 0],[20 -10],[15 30]]`
`⇒3X = [[40 0],[20 -10],[15 30]]-[[4 -4],[8 4],[-10 2]]`
`⇒3X=[[40-4 0+4],[20 -8 -10-4],[15+20 30-2]],`
`⇒ 3X=[[36 4],[12 -14],[25 28]]`
`⇒ X = 1/2 [[36 4],[12 -14],[25 28]]`
`⇒=[[12 4/3],[4 (-14)/3],[25/3 28/3]]`
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