`if A=[{:(3,-2),(7,1):}]and B=[{:(2,3),(-1,4):}],`then find
`(i) A+B (ii) A-2B`

Explanation

To solve the given problem, we need to perform two operations on the matrices \( A \) and \( B \).

Given:
\[ A = \begin{pmatrix} 3 & -2 \\ 7 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} 2 & 3 \\ -1 & 4 \end{pmatrix} \]

### (i) Finding \( A + B \)

To add two matrices, we add their corresponding elements.

1. **Add the elements of \( A \) and \( B \)**:
\[ A + B = \begin{pmatrix} 3 + 2 & -2 + 3 \\ 7 + (-1) & 1 + 4 \end{pmatrix} \]

2. **Calculate each element**:
- First element: \( 3 + 2 = 5 \)
- Second element: \( -2 + 3 = 1 \)
- Third element: \( 7 + (-1) = 6 \)
- Fourth element: \( 1 + 4 = 5 \)

3. **Combine the results**:
\[ A + B = \begin{pmatrix} 5 & 1 \\ 6 & 5 \end{pmatrix} \]

### (ii) Finding \( A - 2B \)

To find \( A - 2B \), we first need to calculate \( 2B \).

1. **Multiply each element of \( B \) by 2**:
\[ 2B = 2 \times \begin{pmatrix} 2 & 3 \\ -1 & 4 \end{pmatrix} = \begin{pmatrix} 2 \times 2 & 2 \times 3 \\ 2 \times (-1) & 2 \times 4 \end{pmatrix} = \begin{pmatrix} 4 & 6 \\ -2 & 8 \end{pmatrix} \]

2. **Now, subtract \( 2B \) from \( A \)**:
\[ A - 2B = \begin{pmatrix} 3 & -2 \\ 7 & 1 \end{pmatrix} - \begin{pmatrix} 4 & 6 \\ -2 & 8 \end{pmatrix} \]

3. **Subtract the corresponding elements**:
\[ A - 2B = \begin{pmatrix} 3 - 4 & -2 - 6 \\ 7 - (-2) & 1 - 8 \end{pmatrix} \]

4. **Calculate each element**:
- First element: \( 3 - 4 = -1 \)
- Second element: \( -2 - 6 = -8 \)
- Third element: \( 7 - (-2) = 7 + 2 = 9 \)
- Fourth element: \( 1 - 8 = -7 \)

5. **Combine the results**:
\[ A - 2B = \begin{pmatrix} -1 & -8 \\ 9 & -7 \end{pmatrix} \]

### Final Answers:
\[ (i) A + B = \begin{pmatrix} 5 & 1 \\ 6 & 5 \end{pmatrix} \]
\[ (ii) A - 2B = \begin{pmatrix} -1 & -8 \\ 9 & -7 \end{pmatrix} \]