Construct a `2xx2` matrix whose elements `a_(ij)` are given by `a_(ij)=i+j`.

Answer

To construct a \(2 \times 2\) matrix whose elements \(a_{ij}\) are given by the formula \(a_{ij} = i + j\), we will follow these steps:

### Step-by-Step Solution:

1. **Define the Matrix**:
We denote the matrix as \(A\) and it will have the order \(2 \times 2\). This means it will have 2 rows and 2 columns.

\[ A = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} \]

2. **Calculate Each Element**:
We will calculate each element of the matrix using the formula \(a_{ij} = i + j\).

- **Element \(a_{11}\)**:
- Here, \(i = 1\) and \(j = 1\).
- \(a_{11} = 1 + 1 = 2\).

- **Element \(a_{12}\)**:
- Here, \(i = 1\) and \(j = 2\).
- \(a_{12} = 1 + 2 = 3\).

- **Element \(a_{21}\)**:
- Here, \(i = 2\) and \(j = 1\).
- \(a_{21} = 2 + 1 = 3\).

- **Element \(a_{22}\)**:
- Here, \(i = 2\) and \(j = 2\).
- \(a_{22} = 2 + 2 = 4\).

3. **Construct the Matrix**:
Now we can fill in the values we calculated into the matrix \(A\):

\[ A = \begin{pmatrix} 2 & 3 \\ 3 & 4 \end{pmatrix} \]

### Final Answer:
The constructed \(2 \times 2\) matrix is:

\[ A = \begin{pmatrix} 2 & 3 \\ 3 & 4 \end{pmatrix} \]