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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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We have, `A=[{:(1, 5),(7,12):}]` and `B=[{:(9,1),(7,8):}]`
Let `C=[{:(a,b),(c,d):}] therefore 3A+5B+2C =0`
`rArr [{:(3,15),(21,36):}]+[{:(45 ,5),(35,40):}]+[{:(2a,2b),(2c,2d):}]=[{:(0,0),(0,0):}]`
`rArr [{:(48,2a,20+2b) ,(56+2c, 76+2d):}]=[{:(0,0),(0,0):}]`
`rArr 2a+4B=0rArra=-24`
Also, `20+2b=0rArrb=-10`
`56 +2c=0rArrc=-28`
and `76+2d=0rArrd=-38`
`therefore C=[{:(-24,-10),(-28,-38):}]`
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