Question

If $3A+4B^{T}=\begin{bmatrix}7&-10& 17\\ 0& 6& 31\end{bmatrix}$ and $2B-3A^{T}=\begin{bmatrix}-1& 18\\ 4&-6\\-5&-7\end{bmatrix}$ then $B=$

• A. $\begin{bmatrix}1& 3\\ -1& 0\\ -2&-4\end{bmatrix}$
• B. $\begin{bmatrix}1& 3\\ 1& 0\\ 2& 4\end{bmatrix}$
• C. $\begin{bmatrix}1& 3\\ -1& 0\\ 2& 4\end{bmatrix}$
• D. $\begin{bmatrix}-1&-3\\ 1& 0\\ 2& 4\end{bmatrix}$

Hint:

When solving matrix equations with transposes, transpose one equation to align the terms (A vs $A^{T}$) for easy elimination.

Answer 1

The Correct Option is C