Find a matrix A such that  2A-3B+5C=O, where B=\begin{bmatrix} -2 &2 &0 \\3 &1 &4 \end{bmatrix} and                            
C=\begin{bmatrix} 2 &0 &-2 \\7 &1 &6 \end{bmatrix} 

 

 

 

 
 
 
 
 

Answers (1)

Given   B=\begin{bmatrix} -2 &2 &0 \\ 3 &1 &4 \end{bmatrix}    and    C=\begin{bmatrix} 2 &0 &-2 \\ 7 &1 &6 \end{bmatrix}

2A-3B+5C=O \\ \Rightarrow 2A=3B-5C \\ \Rightarrow A=\frac{3B-5C}{2}

\Rightarrow A=\frac{1}{2}\left (\left [ 3\begin{bmatrix} -2 &2 &0 \\3 &1 &4 \end{bmatrix} \right ] -5\begin{bmatrix} 2 & 0 &-2 \\ 7 &1 &6 \end{bmatrix}\right )

           =\frac{1}{2}\left (\left [ \begin{bmatrix} -6 &6 &0 \\9 &3 &12 \end{bmatrix} \right ] -\begin{bmatrix} 10 & 0 &-10 \\ 35 &5 &30 \end{bmatrix}\right )

  =\frac{1}{2}\left (\begin{bmatrix} -16 &6 &10 \\-26 &-2 &-18 \end{bmatrix} \right )

A=\begin{bmatrix} -8 &3 &5 \\-13 &-1 &-9 \end{bmatrix}

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