Find matrices A and B, where $2A-B=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$ and $A+3B=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$

Find matrices A and B, where 2A-B= 1 -1; 0 1 and A+3B= 1 -1; 0 1

Miscellaneous Exercise 4(B) · Q185

2A-B=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}

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Let $M=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$ (the book prints the SAME target matrix for both equations). Given: $2A-B=M$ ... (1); $A+3B=M$ ... (2).

From (1): $B=2A-M$ . Substitute into (2): $A+3(2A-M)=M\Rightarrow A+6A-3M=M\Rightarrow 7A=4M\Rightarrow A=\tfrac47 M=\begin{bmatrix}4/7 & -4/7\\0 & 4/7\end{bmatrix}$ .

Then $B=2A-M=\begin{bmatrix}8/7-1 & -8/7+1\\0 & 8/7-1\end{bmatrix}=\begin{bmatrix}1/7 & -1/7\\0 & 1/7\end{bmatrix}$ . …

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Q.Find matrices A and B, where $2A-B=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$ and $A+3B=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$

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Q.Find matrices A and B, where 2A−B=[1−101]2A-B=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}2A−B=[10​−11​] and A+3B=[1−101]A+3B=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}A+3B=[10​−11​]

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Q.Find matrices A and B, where $2A-B=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$ and $A+3B=\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$

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