If 3A - B= \begin{bmatrix} 5 &0 \\ 1 & 1 \end{bmatrix} and B = \begin{bmatrix} 4 &3 \\ 2 & 5 \end{bmatrix}, then find the matrix A.

 

 

 

 
 
 
 
 

Answers (1)

Given:    3A - B= \begin{bmatrix} 5 &0 \\ 1 & 1 \end{bmatrix}

                            B = \begin{bmatrix} 4 &3 \\ 2 & 5 \end{bmatrix}

        Let C= \begin{bmatrix} 5 &0 \\ 1 & 1 \end{bmatrix}    \Rightarrow 3A - B = C

                                            \Rightarrow A = \frac{1}{3}(B + C)

        \Rightarrow A = \frac{1}{3} \left (\begin{bmatrix} 4 &3 \\ 2 & 5 \end{bmatrix} + \begin{bmatrix} 5 &0 \\ 1 & 1 \end{bmatrix} \right )                    

                    = \frac{1}{3}\begin{bmatrix} 9 &3 \\ 3 & 6 \end{bmatrix}

                    = \begin{bmatrix} 3 &1 \\ 1 & 2 \end{bmatrix}

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