Question

If 

 

• A. 1
• B. 3
• C. 2
• D. 4

Hint:

For a \( 2 \times 2 \) matrix, the determinant is calculated as \( ad - bc \) for a matrix
 

Answer 1

The Correct Option is C

Step 1: Analyzing the given matrix equation. 
The matrix equation is: 

Step 2: Using the determinant of the matrix. 
The determinant of a \( 2 \times 2 \) matrix is given by: \[ \text{det}(A) = (x - 2y)(x) - (0)(5) \] This simplifies to: \[ \text{det}(A) = x(x - 2y) \] Step 3: Solving for \( y \). 
We are given that the determinant is equal to 0, so: \[ x(x - 2y) = 0 \] This implies that either \( x = 0 \) or \( x - 2y = 0 \). 
Step 4: Conclusion. 
From \( x - 2y = 0 \), we get \( y = \frac{x}{2} \). Substituting the values, we find that \( y = 2 \), corresponding to option (C).