If `[(3-2x,x+1),(2,4)]` is singular, then find the value of x is:

Options

A. 1
B. 0
C. 3
D. `5/2`

Answer

To determine the value of \( x \) for which the matrix

\[ A = \begin{pmatrix} 3 - 2x & x + 1 \\ 2 & 4 \end{pmatrix} \]

is singular, we need to find the determinant of the matrix and set it equal to zero.

### Step 1: Write the determinant of the matrix
The determinant of a 2x2 matrix

\[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \]

is given by the formula:

\[ \text{det}(A) = ad - bc \]

For our matrix \( A \), we have:

- \( a = 3 - 2x \)
- \( b = x + 1 \)
- \( c = 2 \)
- \( d = 4 \)

Thus, the determinant can be calculated as:

\[ \text{det}(A) = (3 - 2x) \cdot 4 - (x + 1) \cdot 2 \]

### Step 2: Simplify the determinant expression
Now, we will simplify the expression:

\[ \text{det}(A) = 4(3 - 2x) - 2(x + 1) \]

Expanding this gives:

\[ \text{det}(A) = 12 - 8x - 2x - 2 \]

Combining like terms results in:

\[ \text{det}(A) = 10 - 10x \]

### Step 3: Set the determinant to zero
Since the matrix is singular, we set the determinant equal to zero:

\[ 10 - 10x = 0 \]

### Step 4: Solve for \( x \)
Now, we solve for \( x \):

\[ 10 = 10x \]

Dividing both sides by 10 gives:

\[ x = 1 \]

### Conclusion
The value of \( x \) for which the matrix is singular is:

\[ \boxed{1} \]