Finding Matrix X
Question:
Given \[ Y=\begin{bmatrix}3 & 2 \\ 1 & 4\end{bmatrix} \] and \[ 2X + Y = \begin{bmatrix}1 & 0 \\ -3 & 2\end{bmatrix} \] Find \(X\).
Given \[ Y=\begin{bmatrix}3 & 2 \\ 1 & 4\end{bmatrix} \] and \[ 2X + Y = \begin{bmatrix}1 & 0 \\ -3 & 2\end{bmatrix} \] Find \(X\).
Solution:
Step 1: Rearrange the equation
\[ 2X = \begin{bmatrix}1 & 0 \\ -3 & 2\end{bmatrix} – \begin{bmatrix}3 & 2 \\ 1 & 4\end{bmatrix} \] \[ 2X = \begin{bmatrix} 1-3 & 0-2 \\ -3-1 & 2-4 \end{bmatrix} = \begin{bmatrix} -2 & -2 \\ -4 & -2 \end{bmatrix} \]Step 2: Divide by 2
\[ X = \frac{1}{2} \begin{bmatrix} -2 & -2 \\ -4 & -2 \end{bmatrix} = \begin{bmatrix} -1 & -1 \\ -2 & -1 \end{bmatrix} \]Final Answer:
\[ \boxed{ \begin{bmatrix} -1 & -1 \\ -2 & -1 \end{bmatrix} } \]