Question

If $3A - B = \begin{bmatrix} 1 & 2 & -1\\ 0 & 1 & -2\\ -1 & 1 & 4 \end{bmatrix} $ and $A^{-1} = \begin{bmatrix} 1 & 2 & 1\\ 0 & 1 & -1\\ 0 & 0 & 1 \end{bmatrix}$, then $B = ?$

• A. $\begin{bmatrix}2 & -8 & -8\\ 0 & 1 & -1\\ 0 & -1 & 1\end{bmatrix}$
• B. $\begin{bmatrix}2 & -8 & -8\\ 0 & 2 & -1\\ 0 & -1 & 2\end{bmatrix}$
• C. $\begin{bmatrix}2 & -8 & -8\\ 0 & 2 & 5\\ 1 & -1 & -1\end{bmatrix}$
• D. $\begin{bmatrix}2 & -8 & -8\\ 0 & 1 & 5\\ 1 & -1 & 1\end{bmatrix}$

Hint:

Use inverse matrices to find $A$, then substitute into given equation.

Answer 1

The Correct Option is C