InterviewSolution
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InterviewSolution
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Construct a `3 xx 4`matrix, whose elements are given by:(i) `a_(i j)=1/2|-3i+j|` (ii) `a_(i j)=2i-j` |
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Answer» Correct Answer - `[(1,1/2,0,1/2),(5/2,2,3/2,1),(4,7/2,3,5/2)]` A `3xx4` matrix is given by `A=[(a_(11),a_(12),a_(13),a_(14)),(a_(21),a_(22),a_(23),a_(24)),(a_(31),a_(32),a_(33),a_(34))]` `a_("ij")=1/2 |-3i+j|, i=1, 2, 3` and `j=1, 2, 3, 4` `:. a_(11)=1/2 |-3xx1+1|=1/2 |-3+1|=1/2|-2|=2/2=1` `a_(21)=1/2|-3xx2+1|=1/2 |-6+1|=1/2|-5|=5/2` `a_(31)=1/2|-3xx3+1|=1/2|-9+1|=1/2|-8|=8/2=4` `a_(12)=1/2 |-3xx1+2|=1/2|-3+2|=1/2 |-1|=1/2` `a_(22)=1/2 |-3xx2+2|=1/2|-6+2|=1/2 |-4|=4/2=2` `a_(32)=1/2 |-3xx3+2|=1/2 |-9+2|=1/2 |-7|=7/2` `a_(13)=1/2 |-3xx1+3|=1/2 |-3+3|=0` `a_(23)=1/2 |-3xx2+3|=1/2 |-6+3|=1/2|-3|=3/2` `a_(33)=1/2|-3xx3+3|=1/2|-9+3|=1/2 |-6|=6/2=3` `a_(14)=1/2 |-3xx1+4|=1/2 |-3+4|=1/2 |1|=1/2` `a_(24)=1/2 |-3xx2+4|=1/2 |-6+4|=1/2 |-2|=2/2=1` `a_(34)=1/2 |-3xx3+4|=1/2 |-9+4|=1/2 |-5|=5/2` Therefore, the required matrix is `A=[(1,1/2,0,1/2),(5/2,2,3/2,1),(4,7/2,3,5/2)]` |
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