Question

Let \(A = [a_{ij}]\) be a 2×2 matrix such that \(aij=\frac{|-3i + j|}{2}\)  then \(a_{21}\) is :

• A. \(-\frac{1}{2}\)
• B. \(\frac{5}{2}\)
• C. \(-\frac{5}{2}\)
• D. \(\frac{1}{2}\)

Answer 1

The Correct Option is B

To find the matrix element \(a_{21}\) for the matrix \(A = [a_{ij}]\) with \(a_{ij}=\frac{|-3i + j|}{2}\), we need to substitute \(i=2\) and \(j=1\) into the expression. The formula gives:

\(a_{21} = \frac{|-3(2) + 1|}{2}\)

Calculate inside the absolute value:

\(-3(2) + 1 = -6 + 1 = -5\)

Take the absolute value:

\(|-5| = 5\)

Divide by 2:

\(a_{21} = \frac{5}{2}\)

Thus, the value of \(a_{21}\) is \(\frac{5}{2}\).