InterviewSolution
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InterviewSolution
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If `A=[{:(" "1,-1," "2),(" "3," "2," "0),(-2," "0," "1):}],B=[{:(3,1),(0,2),(-2,5):}]" and "C=[{:(2,1,-3),(3,0,-1):}` then verify that `(AB)C=A(BC).` |
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Answer» We have `AB=[{:(1,-1,2),(3,2,0),(-2,0,1):}][{:(3,1),(0,2),(-2,5):}]` `=[{:(3-0-4,1-2+10),(9+0-0,3+4+0),(-6+0-2,-2+0+5):}]=[{:(-1,9),(" "9,7),(-8,3):}]` `implies" "(AB)C=[{:(-1,9),(" "9,7),(-8,3):}][{:(2,1,-3),(3,0,-1):}]` `=[{:(-2+27,-1+0,3-9),(18+21,9+0,-27-7),(-16+9,-8+0,24-3):}]=[{:(25,-1,-6),(39,9,-34),(-7,-8,21):}]` Also, `BC=[{:(3,1),(0,2),(-2,5):}][{:(2,1,-3),(3,0,-1):}]` `=[{:(6+3,3+0,-9-1),(0+6,0+0,0-2),(-4+15,-2+0,6-5):}]=[{:(9,3,-10),(6,0,-2),(11,-2,1):}]` `implies" "A(BC)=[{:(1,-1,2),(3,2,0),(-2,0,1):}][{:(9,3,-10),(6,0,-2),(11,-2," "1):}]` `=[{:(9-6+22,3-0-4,-10+2+2),(27+12+0,9+0-0,-30-4+0),(-18+0+11,-6+0-2,20-0+1):}]` `=[{:(25,-1,-6),(39,9,-34),(-7,-8,21):}].` Hence, `(AB)C=A(BC).` |
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