Question

Construct a_{2 × 2} matrix where a_ij = |–2i + 3j|

Answer 1

Let A = ${\displaystyle {\left[\begin{array}{cc}{\text{a}}_{13}& {\text{a}}_{12}\\ {\text{a}}_{21}& {\text{a}}_{22}\end{array}\right]}_{2 \times 2}}$

Given that `a_ij = |–2i + 3j|

a₁₁ = |–2 × 1 + 3 × 1| = 1

a₁₂ = |–2 × 1 + 3 × 2| = 4

a₂₁ = |–2 × 2 + 3 × 1| = –1

a₂₂ = |–2 × 2 + 3 × 2| = 2

Hence, the matrix A = ${\displaystyle \left[\begin{array}{cc}1& 4\\ -1& 2\end{array}\right]}$