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  • Find X and Y, if (ii) 2X + Y = [2 3 4 0] and 3X + 2Y = [2 -2 -1 5]

Q7.    Find X and Y, if

            (ii) 2X + 3Y = \begin{bmatrix} 2 &3 \\ 4 & 0 \end{bmatrix} and 3X + 2Y = \begin{bmatrix} 2 &-2 \\ -1 & 5 \end{bmatrix}

Answers (1)

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        (ii) 2X + 3Y = \begin{bmatrix} 2 &3 \\ 4 & 0 \end{bmatrix} and 3X + 2Y = \begin{bmatrix} 2 &-2 \\ -1 & 5 \end{bmatrix}

            2X + 3Y = \begin{bmatrix} 2 &3 \\ 4 & 0 \end{bmatrix}..........................1

           3X + 2Y = \begin{bmatrix} 2 &-2 \\ -1 & 5 \end{bmatrix}......................2

         Multiply equation 1 by 3 and equation 2 by 2 and subtract them,

         3(2X + 3Y)-2(3X+2Y) = 3 \times \begin{bmatrix} 2 &3 \\ 4 & 0 \end{bmatrix}     - \, \, \, 2\times \begin{bmatrix} 2 &-2 \\ -1 & 5 \end{bmatrix}

         6X + 9Y-6X-4Y= \begin{bmatrix} 6 &9 \\ 12 & 0 \end{bmatrix} - \begin{bmatrix} 4 &-4 \\ -2 & 10 \end{bmatrix}

         9Y-4Y= \begin{bmatrix} 6-4 &9-(-4) \\ 12-(-2) & 0-10 \end{bmatrix}

       5Y= \begin{bmatrix} 2 &13 \\ 14 & -10 \end{bmatrix}

       Y= \begin{bmatrix} \frac{2}{5} &\frac{13}{5} \\ \frac{14}{5} & -2 \end{bmatrix}

      Putting value of Y in equation 1 , we get 

      2X + 3Y = \begin{bmatrix} 2 &3 \\ 4 & 0 \end{bmatrix}

    2X + 3 \begin{bmatrix} \frac{2}{5} &\frac{13}{5} \\ \frac{14}{5} & -2 \end{bmatrix} = \begin{bmatrix} 2 &3 \\ 4 & 0 \end{bmatrix}

   2X + \begin{bmatrix} \frac{6}{5} &\frac{39}{5} \\ \frac{42}{5} & -6 \end{bmatrix} = \begin{bmatrix} 2 &3 \\ 4 & 0 \end{bmatrix}

 2X = \begin{bmatrix} 2 &3 \\ 4 & 0 \end{bmatrix} - \begin{bmatrix} \frac{6}{5} &\frac{39}{5} \\ \frac{42}{5} & -6 \end{bmatrix}

2X = \begin{bmatrix} 2-\frac{6}{5} &3-\frac{39}{5} \\ 4-\frac{42}{5} & 0 -(-6)\end{bmatrix}

 2X = \begin{bmatrix} \frac{4}{5} &-\frac{24}{5} \\ -\frac{22}{5} & 6\end{bmatrix}

 X = \begin{bmatrix} \frac{2}{5} &-\frac{12}{5} \\ -\frac{11}{5} & 3\end{bmatrix}

 

 

 

 

 

 

 

 

 

  

 

 

    

 

 

 

Posted by

seema garhwal

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