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` if `(M^(2)+MN^(2))U` equals the zero matrix, then `U` is the zero matrix |
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Answer» Correct Answer - A::B Given, `MN = NM, M ne N^(2) and M^(2) = N^(4) ` Then, `M^(2) = N^(2)` lt brgt `rArr (M+N^(2)) (M-N^2) = 0` `therefore M+N^(2) = 0 " " [because M ne N^(2)]` `rArr abs( M+ N^(2)) = 0` (a) `abs( M^(2)+ MN^(2)) = abs(M) abs( M+ N^(2)) = 0` `therefore` Option (a) is correct. `( M^(2)+ MN^(2))U = M( M+ N^(2))U = 0` `therefore` Option (b) is correct. (c) `becauseabs( M^(2)+ MN^(2)) =0` from opttion (a) `therefore abs(M^(2) +MN^(2))cancel(ge) 1` `therefore` OPtion (c ) is incorrect. (d)If ` AX = 0 and abs(A) = 0` then X can be non-zero. |
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