InterviewSolution
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InterviewSolution
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Find the value of k so that `A^2=8A+kI` where `A=[(1,0),(-1,7)].` |
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Answer» We have `A^(2)=[{:(1,0),(-1,7):}][{:(1,0),(-1,7):}]=[{:(1-0,0+0),(-1-7,0+49):}]=[{:(1,0),(-8,49):}],` `(8A+kI)=8.[{:(1,0),(-1,7):}]+k.[{:(1,0),(0,1):}]` `=[{:(8,0),(-8,56):}]+[{:(k,0),(0,k):}]=[{:(8+k," "0),(-8,56+k):}]` `:." "A^(2)=8A+kIimplies[{:(1,0),(-8,49):}]=[{:(8+k," "0),(-8,56+k):}]` `implies" "8+k=1" and "56+k=49impliesimpliesk=-7.` Hence, `k=-7`. |
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