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Question
If A =`[[9 1],[7 8]],B=[[1 5],[7 12]]`find matrix C such that 5A + 3B + 2C is a null matrix.
Solution
Given: 5A+3B+2C `[[0 0],[0 0]]`
⇒5 `[[9 1],[7 8]]+ 3[[1 5],[7 12]]+2C=[[0 0],[0 0]]`
⇒ `[[45 5],[35 40]]+ [[3 15],[12 36]]+2C=[[0 0],[0 0]]`
`⇒ [[45+ 3 5+15],[35+21 40+36]]+2C[[0 0],[0 0]]`
`⇒ [[48 20],[56 76]]+2C=[[0 0],[0 0]]`
`⇒ 2C = [[0 0],[0 0]]-[[48 20],[56 76]] `
`⇒ C= 1/2 [[-48 -20],[-56 -76]]`
`⇒ [[-24 -10],[-28 -38]]`
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