Question

Given that \[ \begin{bmatrix} 1 & x \end{bmatrix} \begin{bmatrix} 4 & 0 \\ -2 & 0 \end{bmatrix} = 0 \] then the value of \( x \) is:

• A. \( -4 \)
• B. \( -2 \)
• C. \( 2 \)
• D. \( 4 \)

Hint:

For matrix equations, ensure each resulting element matches the given condition.

Answer 1

The Correct Option is C

Step 1: Matrix multiplication
Perform the matrix multiplication: \[ \begin{bmatrix} 1 & x \end{bmatrix} \begin{bmatrix} 4 & 0 \\ -2 & 0 \end{bmatrix} = \begin{bmatrix} 4 - 2x & 0 \end{bmatrix}. \]
Step 2: Set the result to zero
For the equation to hold, \( 4 - 2x = 0 \).

Step 3: Solve for \( x \)
Rearranging: \[ 4 - 2x = 0 \implies x = \frac{4}{2} = 2. \]
Step 4: Verify the options
The value \( x = 2 \) matches option (C).