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If A=[{:(1,5),(7,12):}] and B=[{:(9,1),(...

If `A=[{:(1,5),(7,12):}]` and `B=[{:(9,1),( 7,8):}]` then find a matrix C such that `3A+5B+2C` is a null matrix.

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Verified by Experts

The correct Answer is:
`[(-24,-10),(-28,-38)]`
We have, `A=[(1,5),(7,12)]` and `B=[(9,1),(7,8)]`
Let `C=[(a,b),(c,d)]`
`:. 3A+5B+2C=O`
`implies [(3,15),(21,36)]+[(45,5),(35,40)]+[(2a,2b),(2c,2d)]=[(0,0),(0,0)]`
`implies [(48+2a,20+2b),(56+2c,76+2d)]=[(0,0),(0,0)]`
So, we have
`2a+48=0implies a=-24`,
`20+2b=0implies b=-10`,
`56+2c=0 implies c=-28` ,
and `76+2d=0 implies d=-38`.
`:. C=[(-24,-10),(-28,-38)]`
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