If `[(2x,3),(0,y-1)]=[(x-3,3),(0,2)]` then the values of x and y respectively are

Options

A. `3,-3`
B. `-3,3`
C. `-3,-3`
D. `3,3`

Answer

To solve the equation given by the matrices \(\begin{pmatrix} 2x & 3 \\ 0 & y-1 \end{pmatrix} = \begin{pmatrix} x-3 & 3 \\ 0 & 2 \end{pmatrix}\), we will equate the corresponding elements of the matrices.

### Step 1: Equate the corresponding elements of the matrices
From the first row, we have:
1. \(2x = x - 3\)
2. \(3 = 3\) (This equation is always true and does not provide any new information)

From the second row, we have:
3. \(0 = 0\) (This equation is also always true)
4. \(y - 1 = 2\)

### Step 2: Solve the first equation \(2x = x - 3\)
To isolate \(x\), we can rearrange the equation:
\[ 2x - x = -3 \]
This simplifies to:
\[ x = -3 \]

### Step 3: Solve the second equation \(y - 1 = 2\)
To isolate \(y\), we can rearrange the equation:
\[ y = 2 + 1 \]
This simplifies to:
\[ y = 3 \]

### Final Values
Thus, the values of \(x\) and \(y\) are:
\[ x = -3, \quad y = 3 \]