find 1x3 matrices x and y such that x+2y=[1 3 -2] and x+y=[2 0 1]

Question

find 1x3 matrices x and y such that x+2y=[1 3 -2] and x+y=[2 0 1]

Answer 1

Set it up and solve it as a system of two linear equations in two variables:

         x + 2y  =  [1  3  -2]
         x  +  y  =  [2  0   1]
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Multiply the second on through by -1 and add it to the first one:

          x  +  2y  =  [1  3  -2]
         -x  -     y  =  [-2 0  -1]
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                     y  =  [-1  3  -3]
    Then         x  =  [2  0  1]  -  [-1  3  -3]

        or         x  =  [3  -3  4]
                    y  =  [-1  3  -3]