If `a_(ij)=|2i + 3j^(2)|,` then matrix `A_(2xx2) = [a_(ij)]` will be:

Options

A. `[(5,-14),(7,16)]`
B. `[(5,14),(-7,16)]`
C. `[(5,14),(7,16)]`
D. `[(5,14),(7,-16)]`

Answer

To construct the matrix \( A \) of order \( 2 \times 2 \) given the elements defined by \( a_{ij} = |2i + 3j^2| \), we need to calculate each element of the matrix based on the values of \( i \) and \( j \).

### Step-by-Step Solution:

1. **Identify the Matrix Elements**:
The matrix \( A \) will have the following elements:
\[ A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} \]
where \( a_{ij} = |2i + 3j^2| \).

2. **Calculate \( a_{11} \)**:
For \( i = 1 \) and \( j = 1 \):
\[ a_{11} = |2(1) + 3(1)^2| = |2 + 3| = |5| = 5 \]

3. **Calculate \( a_{12} \)**:
For \( i = 1 \) and \( j = 2 \):
\[ a_{12} = |2(1) + 3(2)^2| = |2 + 3 \times 4| = |2 + 12| = |14| = 14 \]

4. **Calculate \( a_{21} \)**:
For \( i = 2 \) and \( j = 1 \):
\[ a_{21} = |2(2) + 3(1)^2| = |4 + 3| = |7| = 7 \]

5. **Calculate \( a_{22} \)**:
For \( i = 2 \) and \( j = 2 \):
\[ a_{22} = |2(2) + 3(2)^2| = |4 + 3 \times 4| = |4 + 12| = |16| = 16 \]

6. **Construct the Matrix**:
Now that we have all the elements, we can construct the matrix \( A \):
\[ A = \begin{bmatrix} 5 & 14 \\ 7 & 16 \end{bmatrix} \]

### Final Answer:
The matrix \( A \) is:
\[ A = \begin{bmatrix} 5 & 14 \\ 7 & 16 \end{bmatrix} \]