If `[(x,1)][(1,0),(-2,0)]` = 0, then x equals

Options

A. 0
B. `-2`
C. `-1`
D. 2

Answer

To solve the equation given by the matrix multiplication \(\begin{pmatrix} x & 1 \end{pmatrix} \begin{pmatrix} 1 & 0 \\ -2 & 0 \end{pmatrix} = \begin{pmatrix} 0 & 0 \end{pmatrix}\), we will follow these steps:

### Step 1: Matrix Multiplication
We start by multiplying the two matrices. The first matrix is a \(1 \times 2\) matrix and the second matrix is a \(2 \times 2\) matrix. The resulting matrix will also be a \(1 \times 2\) matrix.

\[ \begin{pmatrix} x & 1 \end{pmatrix} \begin{pmatrix} 1 & 0 \\ -2 & 0 \end{pmatrix} = \begin{pmatrix} x \cdot 1 + 1 \cdot (-2) & x \cdot 0 + 1 \cdot 0 \end{pmatrix} \]

### Step 2: Simplifying the Result
Now we simplify the multiplication:

\[ = \begin{pmatrix} x - 2 & 0 \end{pmatrix} \]

### Step 3: Setting the Result Equal to the Zero Matrix
According to the problem, this result must equal the zero matrix:

\[ \begin{pmatrix} x - 2 & 0 \end{pmatrix} = \begin{pmatrix} 0 & 0 \end{pmatrix} \]

### Step 4: Solving for x
From the equality of the matrices, we can set up the following equation:

\[ x - 2 = 0 \]

Now, solve for \(x\):

\[ x = 2 \]

### Conclusion
Thus, the value of \(x\) is \(2\).

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