InterviewSolution
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InterviewSolution
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If `A=[[2,a,-3] , [0,2,5] , [1,1,3]]` then,find the value of a for which `A^(-1)` exists.A. `a=2`B. `a!=2`C. `a!=-2`D. none of these |
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Answer» Correct Answer - D We have `A=|(2, lamda, -3),(0,2,5),(1,1,3)|` Expanding along `R_(1)` `|A|=2(6-5)-lamda(-5)-3(-2)=2+5lamda+6` We know that `A^(-1)` exists if `A` is non singular matrix i.e. `|A|!=0` `:.2+5lamda+6!=0` `implies 5lamda!=-8` `:. lamda!=(-8)/5` So, `A^(-1)` exists if and only if `lamda!=(-8)/5`. |
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