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 problem, we need to compare the corresponding elements of the two matrices given in the equation:

\[ \begin{pmatrix} 2x + y & 3y \\ 0 & 4 \end{pmatrix} = \begin{pmatrix} 6 & 0 \\ 0 & 4 \end{pmatrix} \]

### Step 1: Set up the equations by comparing corresponding elements.

From the first row, we have:
1. \(2x + y = 6\) (from the first column)
2. \(3y = 0\) (from the second column)

From the second row, we have:
3. \(0 = 0\) (which is always true and does not provide any new information)
4. \(4 = 4\) (which is also always true)

### Step 2: Solve the second equation for \(y\).

From equation 2:
\[ 3y = 0 \]
Dividing both sides by 3 gives:
\[ y = 0 \]

### Step 3: Substitute the value of \(y\) into the first equation.

Now substitute \(y = 0\) into equation 1:
\[ 2x + 0 = 6 \]
This simplifies to:
\[ 2x = 6 \]

### Step 4: Solve for \(x\).

Dividing both sides by 2 gives:
\[ x = \frac{6}{2} = 3 \]

### Conclusion

The value of \(x\) is:
\[ \boxed{3} \]

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