Solved the following equation for x :
`["x 1"][(1,0),(-2,0)]=O`

Answer

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

### Step 1: Identify the matrices involved
We have a \(1 \times 2\) matrix \(\begin{bmatrix} x & 1 \end{bmatrix}\) and a \(2 \times 2\) matrix \(\begin{bmatrix} 1 & 0 \\ -2 & 0 \end{bmatrix}\).

### Step 2: Perform the matrix multiplication
To multiply the matrices, we will use the rule of matrix multiplication (row by column):

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

Calculating each element:
- First element: \(x \cdot 1 + 1 \cdot (-2) = x - 2\)
- Second element: \(x \cdot 0 + 1 \cdot 0 = 0\)

Thus, the result of the multiplication is:

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

### Step 3: Set the result equal to the null matrix
We know that this result must equal the null matrix \(O\), which for a \(1 \times 2\) matrix is:

\[ \begin{bmatrix} 0 & 0 \end{bmatrix} \]

So we set up the equation:

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

### Step 4: Solve the equations
From the equality of the matrices, we can derive the following equations:

1. \(x - 2 = 0\)
2. \(0 = 0\) (which is always true)

Now, solving the first equation:

\[ x - 2 = 0 \implies x = 2 \]

### Final Answer
Thus, the solution for \(x\) is:

\[ \boxed{2} \]