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InterviewSolution
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Find the matrix X so that `X[1 2 3 4 5 6]=[-7-8-9""""""2""""""4""""6]` |
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Answer» Correct Answer - `X=[(1,-2),(2,0)]` It is given that `X[(1,2,3),(4,5,6)]=[(-7,-8,-9),(2,4,6)]` The matrix given on the R.H.S. of the equation is a `2xx3` matrix and the one given on the L.H.S is a `2xx3` matrix. Therefore, X has to be a `2xx2` matrix. Now, let `X=[(a,c),(b,d)]` therefore, we have `[(a,c),(b,d)][(1,2,3),(4,5,6)]=[(-7,-8,-9),(2,4,6)]` or `[(a+4c,2a+5c,3a+6c),(b+4d,2b+5d,3b+6d)]=[(-7,-8,-9),(2,4,6)]` Equating the corresponding elements of the two matrices, we have `{:(a+4c=-7",",2a+5c=-8",",3a+6c=-9),(b+4d=2",",2b+5d=4",",3b+6d=6):}` Now, `a+4c=-7 implies a=-7-4c` `:. 2a+5c=-8 implies -14-8c+5c=-8` or `-3c=6` or `c=-2` `:. a=-7-4(-2)=-7+8=1` Now, `b+4d=2` or `b=2-4d` `:. 2b+2d=4implies 4-8d+5d=4` `implies -3d=0` `d=0` `:. b=2-4(0)=2` Thus, `a=1, b=2, c=-2, d=0` Hence, the required matrix X is `[(1,-2),(2,0)]` |
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