Question

Construct a 2 × 2 matrix A = [a_ij] whose elements a_ij are given by $a_{ij}=\left\{\begin{array}{ll}\frac{\left|-3i+j\right|}{2}& ,\mathrm{if}i\ne j\\ {\left(i+j\right)}^2& ,\mathrm{if}i=j\end{array}\right.$

Answer 1

Given: $a_{ij}=\left\{\begin{array}{ll}\frac{\left|-3i+j\right|}{2}& ,\mathrm{if}i\ne j\\ {\left(i+j\right)}^2& ,\mathrm{if}i=j\end{array}\right.$

$$\begin{gathered} a_{11}={\left(1+1\right)}^2=4 \\ {a}_{12}=\frac{\left|-3\times 1+2\right|}{2}=\frac{1}{2} \\ {a}_{21}=\frac{\left|-3\times 2+1\right|}{2}=\frac{5}{2} \\ {a}_{22}={\left(2+2\right)}^2=16 \\ \mathrm{Hence},\mathrm{the}\mathrm{matrix}A=\left[\begin{array}{cc}4& \frac{1}{2}\\ \frac{5}{2}& 16\end{array}\right]. \end{gathered}$$