Q7.    Find X and Y, if

            (i) X + Y = \begin{bmatrix} 7 &0 \\ 2 &5 \end{bmatrix} and X - Y = \begin{bmatrix} 3 &0 \\ 0 &3 \end{bmatrix}

Answers (1)

      (i) The given matrices are

 X + Y = \begin{bmatrix} 7 &0 \\ 2 &5 \end{bmatrix}     and    X - Y = \begin{bmatrix} 3 &0 \\ 0 &3 \end{bmatrix}

         X + Y = \begin{bmatrix} 7 &0 \\ 2 &5 \end{bmatrix}.............................1 

        X - Y = \begin{bmatrix} 3 &0 \\ 0 &3 \end{bmatrix}.............................2

         Adding equation 1 and 2, we get 

         2 X = \begin{bmatrix} 7 &0 \\ 2 &5 \end{bmatrix} + \begin{bmatrix} 3 &0 \\ 0 &3 \end{bmatrix}

         2 X = \begin{bmatrix} 7+3 &0+0 \\ 2+0 &5+3 \end{bmatrix}

         2 X = \begin{bmatrix} 10 &0 \\ 2 &8 \end{bmatrix}

           X = \begin{bmatrix} 5 &0 \\ 1 &4 \end{bmatrix}

   Putting the value of X in equation 1, we get 

     \begin{bmatrix} 5 &0 \\ 1 &4 \end{bmatrix} +Y = \begin{bmatrix} 7 &0 \\ 2 &5 \end{bmatrix}

    Y = \begin{bmatrix} 7 &0 \\ 2 &5 \end{bmatrix} -  \begin{bmatrix} 5 &0 \\ 1 &4 \end{bmatrix}

   Y = \begin{bmatrix} 7-5 &0-0 \\ 2-1 &5-4 \end{bmatrix}

  Y = \begin{bmatrix} 2 &0 \\ 1 &1 \end{bmatrix}

 

 

 

 

 

 

 

 

 

 

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