Given `[{:(,x,y+2),(,3,z-1):}] =[{:(,3,1),(,3,2):}]` find x,y and z.

Answer

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

### Step-by-step Solution:

1. **Equate the first elements:**
\[ x = 3 \]

2. **Equate the second elements of the first row:**
\[ y + 2 = 1 \]
To solve for \(y\), subtract 2 from both sides:
\[ y = 1 - 2 = -1 \]

3. **Equate the first element of the second row:**
\[ 3 = 3 \]
This equation is always true and does not provide any new information.

4. **Equate the second elements of the second row:**
\[ z - 1 = 2 \]
To solve for \(z\), add 1 to both sides:
\[ z = 2 + 1 = 3 \]

### Final Values:
Thus, we have:
- \(x = 3\)
- \(y = -1\)
- \(z = 3\)

### Summary:
The values are:
- \(x = 3\)
- \(y = -1\)
- \(z = 3\)