If \(A = \begin{bmatrix}2&-2&1\\0&4&2\end{bmatrix}\) and \(B=\begin{bmatrix}1&-2&7\\2&0&6\end{bmatrix}\) are two matrices such that \(3A - 2B + 4C = O\), then matrix \(C\) is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\begin{bmatrix}-1&1/2&11/4\\1&-3&3/2\end{bmatrix}\)
Here O is the zero matrix. Solving for C:
\(4C = 2B - 3A\)
\( \displaystyle 2B = \begin{bmatrix}2&-4&14\\4&0&12\end{bmatrix} \)
\( \displaystyle 3A = \begin{bmatrix}6&-6&3\\0&12&6\end{bmatrix} \)
Subtracting entry by entry:
\( \displaystyle 2B - 3A = \begin{bmatrix}-4&2&11\\4&-12&6\end{bmatrix} \)
Dividing every entry by 4:
\( \displaystyle C = \begin{bmatrix}-1&1/2&11/4\\1&-3&3/2\end{bmatrix} \)