InterviewSolution
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InterviewSolution
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Let `P=[a_("ij")]` be a `3xx3` matrix and let `Q=[b_("ij")]`, where `b_("ij")=2^(i+j) a_("ij")` for `1 le i, j le 3`. If the determinant of P is 2, then the determinant of the matrix Q isA. `2^(10)`B. `2^(11)`C. `2^(12)`D. `2^(13)` |
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Answer» Correct Answer - D `|Q|=|(2^(2)a_(11),2^(3)a_(12),2^(2)a_(13)),(2^(3)a_(21),2^(4) a_(22),2^(5) a_(23)),(2^(4) a_(31),2^(5) a_(32),2^(6) a_(33))|` `=2^(2). 2^(3). 2^(4)|(a_(11),a_(12),a_(13)),(2a_(21),2a_(22),2a_(23)),(2^(2)a_(31),2^(2)a_(32),2^(2) a_(33))|` `=2^(9). 2. 2^(2) |(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))|` `=2^(12) |P|` `=2^(13)` |
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