Question

If A = [a_ij] = $\left[\begin{array}{ccc}2& 3& -5\\ 1& 4& 9\\ 0& 7& -2\end{array}\right]$ and B = [b_ij] = $\left[\begin{array}{cc}2& -1\\ -3& 4\\ 1& 2\end{array}\right]$
then find (i) a₂₂ + b₂₁ (ii) a₁₁ b₁₁ + a₂₂ b₂₂

Answer 1

$\left(i\right)$

$a_{22}+b_{21}$

$$\begin{gathered} \mathrm{Here}, \\ {a}_{22}=4\mathrm{and}{b}_{21}=-3 \\ \Rightarrow a_{22}+b_{21}=4-3=1 \end{gathered}$$

$\left(ii\right)$

$a_{11}{b}_{11}+a_{22}{b}_{22}$

$$\begin{gathered} \mathrm{Here}, \\ {a}_{11}=2,b_{11}=2,a_{22}=4\mathrm{and}{b}_{22}=4 \\ \Rightarrow a_{11}{b}_{11}+a_{22}{b}_{22}=2\times 2+4\times 4 \\ \Rightarrow a_{11}{b}_{11}+a_{22}{b}_{22}=4+16 \\ \Rightarrow a_{11}{b}_{11}+a_{22}{b}_{22}=20 \end{gathered}$$