Q.6    Find the values of x, y and z from the following equations:

        (ii)

             \begin{bmatrix} x +y & 2\\ 5 + z & xy \end{bmatrix} = \begin{bmatrix} 6 &2 \\ 5 & 8 \end{bmatrix}

Answers (1)

        (ii)

             \begin{bmatrix} x +y & 2\\ 5 + z & xy \end{bmatrix} = \begin{bmatrix} 6 &2 \\ 5 & 8 \end{bmatrix}

If two matrices are equal, then their corresponding elements are also equal. 

         \therefore    x+y=6   \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot (i)

                x=6-y     

                  xy=8     \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot (ii)

  Solving equation (i)  and (ii) ,             

              (6-y)y =8

              6y-y^{2}=8

                y^{2}-6y+8=0

 solving this equation we get,

 y=4 \, \, and\, \, y=2

  Putting the values of y, we get 

   x=2 \, \, and\, \, x=4

And also equating the first element of the second raw

   5+z = 5,    z=0

  Hence,   

  x=2,y=4,z=0\, \, \, \, \, and\, \, \, \, \, \, x=4,y=2,z=0

               

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