If `[(2x+y,3y),(0,4)]=[(6,0),(0,4)]` , then find the value of x .

Options

A. 2
B. 3
C. `-1`
D. 0

Answer

To solve the equation given by the matrices \([(2x+y, 3y), (0, 4)] = [(6, 0), (0, 4)]\), we need to equate the corresponding elements of the two matrices.

### Step-by-Step Solution:

1. **Set up the equations**:
From the equality of the matrices, we can write the following equations based on corresponding elements:
- From the first element: \(2x + y = 6\) (Equation 1)
- From the second element: \(3y = 0\) (Equation 2)
- The third elements \(0 = 0\) and the fourth elements \(4 = 4\) are trivially true and do not provide additional information.

2. **Solve Equation 2 for \(y\)**:
From Equation 2, we can solve for \(y\):
\[ 3y = 0 \implies y = 0 \]

3. **Substitute \(y\) into Equation 1**:
Now that we have \(y = 0\), we substitute this value into Equation 1:
\[ 2x + 0 = 6 \implies 2x = 6 \]

4. **Solve for \(x\)**:
Now, we can solve for \(x\):
\[ x = \frac{6}{2} = 3 \]

5. **Conclusion**:
Thus, the value of \(x\) is \(3\).

### Final Answer:
The value of \(x\) is \(3\).