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Answer» If `A` is a `nxxn` matrix such that `a_(ij)=(i^(2)+j^(2)-5ij).(j-i)Aai` and `j` then trace `(A)=0` If `A` is a `nxxn` matrix such that `a_(ij)=(i^(2)+j^(2)-5ij).(j-i)Aai` and `j` then trace `(A)!=0` If `P` is a `3xx3` ORTHOGONAL matrix, `alpha, beta, gamma` are the ANGLES made by a straight line with `OX, OY, OZ` and `A=[(sin^(2)alpha, sinalpha.sinbeta, sinalpha.singamma), (sinalpha.sinbeta, sin^(2)beta, sinbeta.singamma), (sinalpha.singamma, sinbeta.singamma, sin^(2)gamma)]` and `Q=P^(T)AP`, then `PQ^(6)P^(T)=32A` If matrix `A=[a_(ij)]_(3xx3)` and matrix `B=[b_(ij)]_(3xx3)` where `a_(ij)+a_(ji)=0` and `b_(ij)-b_(ji)=0 AA i` and `j` then `A^(6)B^(7)` is a singular matrix Solution :(A) `a_(ij)=-a_(ji)impliesa_(ij)+a_(ji)=0impliesA` is skew symmetric matrix (C) `A^(2)=2AimpliesA^(3)=2^(2)impliesA^(6)=2^(5)A` (D) `A^(6)B^(7)` is a skew symmetric matrix of odd order
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