📘 Question
Solve the matrix equation:
\[
\begin{bmatrix}x & 1\end{bmatrix}
\begin{bmatrix}1 & 0 \\ -2 & 0\end{bmatrix}
=
O
\]
Find the value of \(x\), where \(O\) is the zero matrix.
✏️ Step-by-Step Solution
Step 1: Perform matrix multiplication
\[
\begin{bmatrix}x & 1\end{bmatrix}
\begin{bmatrix}1 & 0 \\ -2 & 0\end{bmatrix}
=
\begin{bmatrix}x(1) + 1(-2) \quad x(0) + 1(0)\end{bmatrix}
\]
\[
=
\begin{bmatrix}x – 2 \quad 0\end{bmatrix}
\]
Step 2: Equate to zero matrix
\[
\begin{bmatrix}x – 2 \quad 0\end{bmatrix}
=
\begin{bmatrix}0 \quad 0\end{bmatrix}
\]
Step 3: Solve
\[ x – 2 = 0 \Rightarrow x = 2 \]
✅ Final Answer
\[
\boxed{2}
\]
💡 Key Concept
If the product of matrices equals a zero matrix, then each corresponding element must be zero. Solve by performing multiplication and equating elements.