InterviewSolution
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InterviewSolution
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Lat`A = [a_(ij)]_(3xx 3).` If tr is arithmetic mean of elements of rth row and `a_(ij )+ a_( jk) + a_(ki)=0` holde for all `1 le i, j, k le 3.` Matrix A isA. non- singularB. symmetricC. skew-symmetricD. nether symmetric nor skew-symmetric |
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Answer» Correct Answer - C `therefore A = [[a_(11) , a_(12),a_(13)],[a_(21),a_(22), a_(23) ],[a_(31), a_(32),a_(33)]]` `rArr t_(1) = (a_(11) + a_(12)+a_(23))/3 = 0, [because a_(ij) + a_(jk) + a_(ki)=0]` `t_(2) = (a_(21) + a_(22) + a_(23))/3 = 0` and `t_(3) = (a_(31) + a_(32) + a_(33))/3 = 0` `because a_(11) + a_(11) + a_(11) = 0, a_(11) + a_(12) + a_(21)= 0,` ` a_(11) + a_(13) + a_(31) = 0, a_(22) + a_(22) + a_(22)= 0, ` ` a_(22) + a_(12) + a_(21) = 0, a_(22) + a_(22) + a_(22)= 0, ` ` a_(33) + a_(13) + a_(31) = 0, a_(33) + a_(23) + a_(32)= 0, ` and ` a_(33) + a_(12) + a_(21) = 0,` we get `a_(11) = a_(22) = a_(33) = 0 ` and `a_(12) =-a_(21), a_(23) = - a_(32), a_(13) = -a_(31)` Hence, A is skew - symmetric matrix. |
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