Question

Solve for \( x \) in the determinant equation: \[ \left| \begin{matrix} x & 15 \\ 4 & 15 \end{matrix} \right| = 0 \]

• A. 15
• B. -15
• C. 12
• D. 60

Hint:

To solve a determinant equation for \( x \), calculate the determinant and set it equal to 0, then solve for \( x \).

Answer 1

The Correct Option is A

We are given the matrix equation: \[ \left| \begin{matrix} x & 15 \\ 4 & 15 \end{matrix} \right| = 0 \] The determinant of this 2x2 matrix is: \[ \text{det} = (x \times 15) - (15 \times 4) = 15x - 60 \] Set the determinant equal to 0: \[ 15x - 60 = 0 \] Solve for \( x \): \[ 15x = 60 \] \[ x = \frac{60}{15} = 15 \] Thus, the correct answer is \( 15 \).