Construct a `3xx2` matrix whose elements in the ith row and jth column are given by :
`a_(ij)=(i+4j)/(2)`

Answer

To construct a \(3 \times 2\) matrix whose elements in the \(i\)th row and \(j\)th column are given by the formula:

\[ a_{ij} = \frac{i + 4j}{2} \]

we will compute the values for each element in the matrix step by step.

### Step 1: Define the dimensions of the matrix
We need to create a matrix with 3 rows and 2 columns. Thus, the values of \(i\) (row index) will be \(1, 2, 3\) and the values of \(j\) (column index) will be \(1, 2\).

### Step 2: Calculate each element of the matrix

1. **Calculate \(a_{11}\)**:
\[ a_{11} = \frac{1 + 4 \cdot 1}{2} = \frac{1 + 4}{2} = \frac{5}{2} \]

2. **Calculate \(a_{12}\)**:
\[ a_{12} = \frac{1 + 4 \cdot 2}{2} = \frac{1 + 8}{2} = \frac{9}{2} \]

3. **Calculate \(a_{21}\)**:
\[ a_{21} = \frac{2 + 4 \cdot 1}{2} = \frac{2 + 4}{2} = \frac{6}{2} = 3 \]

4. **Calculate \(a_{22}\)**:
\[ a_{22} = \frac{2 + 4 \cdot 2}{2} = \frac{2 + 8}{2} = \frac{10}{2} = 5 \]

5. **Calculate \(a_{31}\)**:
\[ a_{31} = \frac{3 + 4 \cdot 1}{2} = \frac{3 + 4}{2} = \frac{7}{2} \]

6. **Calculate \(a_{32}\)**:
\[ a_{32} = \frac{3 + 4 \cdot 2}{2} = \frac{3 + 8}{2} = \frac{11}{2} \]

### Step 3: Construct the matrix
Now we can write the computed values in matrix form:

\[ A = \begin{bmatrix} \frac{5}{2} & \frac{9}{2} \\ 3 & 5 \\ \frac{7}{2} & \frac{11}{2} \end{bmatrix} \]

### Final Answer
Thus, the \(3 \times 2\) matrix is:

\[ A = \begin{bmatrix} \frac{5}{2} & \frac{9}{2} \\ 3 & 5 \\ \frac{7}{2} & \frac{11}{2} \end{bmatrix} \]