InterviewSolution
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InterviewSolution
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Let m and N be two 3x3 matrices such that MN=NM. Further if `M!=N^2` and `M^2=N^4` then which of the following are correct.A. determinant of `(M^(2)+Mn^(2))` is 0B. there is a `3xx3` non-zero matrix U such that `(M^(2)+MN^(2))U` is the zero matrixC. determinant of `(M^(2)+MN^(2)) ge 1`D. for a `3xx3` matrix `U`, is the zero matrix |
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Answer» Correct Answer - A::B `M^(2)=N^(4)` `implies M^(2)-N^(4)=O` `implies (M-N^(2)) (M+N^(2))=O" "` (as M, N commute) Also, `M ne N^(2)`. det. `((M-N^(2))(M+N^(2)))=0` as `M ne N^(2) implies` dte. `(M+N^(2))=0` Also, det `(M^(2)+MN^(2))=("det. M") ("det. "(M+N^(2)))=0` Hence, there exist non-null U such that `(M^(2)+MN^(2)) U=O`. |
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