Question

If \[ A = \begin{bmatrix} 2 & 4 \\ x & 2 \end{bmatrix} \] and $A$ is singular, then $x$ is equal to:

• A. $\frac{1}{4}$
• B. -7
• C. $-\frac{1}{4}$
• D. 32

Answer 1

The Correct Option is C

To determine the value of \(x\), we use the fact that \(A\) is singular. A matrix is singular if its determinant is zero. The given matrix is:

\[ A = \begin{bmatrix} 2 & 4 \\ x & -\frac{1}{2} \end{bmatrix}. \]

The determinant of \(A\) is:

\[ \text{det}(A) = (2)(-1) - (x)(4) = -2 - 4x. \]

Set \(\text{det}(A) = 0\) because \(A\) is singular:

\[ -2 - 4x = 0. \]

Solve for \(x\):

\[ 4x = -2 \implies x = -\frac{1}{4}. \]

Thus, \(x = -\frac{1}{4}\).