The elements `a_(ij)` of a `2xx2` matrix are given by `a_(ij) = (1)/(4) |-3 i + j|`. Then, the value of element `a_(21)` is:

Options

A. `-(5)/(4)`
B. `-(1)/(4)`
C. `(1)/(4)`
D. `(5)/(4)`

Answer

To find the value of the element \( a_{21} \) of the given \( 2 \times 2 \) matrix defined by the formula \( a_{ij} = \frac{1}{4} |-3i + j| \), we will follow these steps:

### Step-by-step Solution:

1. **Identify the indices for \( a_{21} \)**:
- Here, \( i = 2 \) and \( j = 1 \).

2. **Substitute the values of \( i \) and \( j \) into the formula**:
\[ a_{21} = \frac{1}{4} |-3(2) + 1| \]

3. **Calculate the expression inside the modulus**:
- First, compute \( -3(2) + 1 \):
\[ -3(2) = -6 \]
\[ -6 + 1 = -5 \]

4. **Take the modulus of the result**:
\[ |-5| = 5 \]

5. **Multiply by \( \frac{1}{4} \)**:
\[ a_{21} = \frac{1}{4} \times 5 = \frac{5}{4} \]

Thus, the value of the element \( a_{21} \) is \( \frac{5}{4} \).