InterviewSolution
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InterviewSolution
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If `A = [(3,1),(2,1)]` find the value of `|a|+|b|` such that `A^(2)+aA+bl=O.` Hece,find `A^(-1)` |
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Answer» we have, `A=[(3,1),(2,0)]` then `|A|=|(3,1),(2,1)|=3-2=1!=0` `therefore" " A^(-1)`. Exists. Now `A^(2)=A.A=[(3,1),(2,1)][(3,1),(2,1)]=[(11,4),(8,3)]` `rArr" " [(11,4),(8,3)]+a[(3,1),(2,1)]+b[(1,0),(0,1)]=[(0,0),(0,0)]` `rArr" " [(11+3a+b,4+a),(8+2a,3+a+b)]+[(0,0),(0,0)]` Equating the corresponding elements, we get `11a+3a+b=0` `4+a=0` ` 3+a+b=0` from Eqs. (ii) and (iv), we get `a=-4` and `b=1` `therefore" " |a|+|b|=|-4|+|1|=4+1=5` As`" " A^(2)+aA+bI=O` ` rArr " " A^(2)-4A+I+O rArr I=4A-A^(2)` `rArr " " IA^(-1) = 4(A A^(-1))-A(A A^(-1))` `=4I-AI=4I-A` `= 4[(1,0),(0,1)]-[(3,1),(2,1)]=[(4,0),(0,4)]-[(3,1),(2,1)]` `therefore " " A(-1)=[(1,-1),(-2,3)]` |
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