In the matrix `A=[(3-2x,x+1),(2,4)]` is singular then X=?

Options

A. 0
B. 1
C. -1
D. -2

Explanation

To find the value of \( x \) for which the matrix \( A = \begin{pmatrix} 3 - 2x & x + 1 \\ 2 & 4 \end{pmatrix} \) is singular, we need to calculate the determinant of the matrix and set it equal to zero.

### Step-by-Step Solution:

1. **Write down the determinant formula for a 2x2 matrix**:
The determinant of a matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by:
\[ \text{det}(A) = ad - bc \]

2. **Identify the elements of the matrix**:
For our matrix \( A \):
- \( a = 3 - 2x \)
- \( b = x + 1 \)
- \( c = 2 \)
- \( d = 4 \)

3. **Substitute the elements into the determinant formula**:
\[ \text{det}(A) = (3 - 2x) \cdot 4 - (x + 1) \cdot 2 \]

4. **Expand the determinant**:
\[ \text{det}(A) = 12 - 8x - 2(x + 1) \]
\[ = 12 - 8x - 2x - 2 \]
\[ = 12 - 2 - 10x \]
\[ = 10 - 10x \]

5. **Set the determinant equal to zero for the matrix to be singular**:
\[ 10 - 10x = 0 \]

6. **Solve for \( x \)**:
\[ 10 = 10x \]
\[ x = 1 \]

### Final Answer:
The value of \( x \) for which the matrix \( A \) is singular is \( x = 1 \).