Solve this

Question:

If $A=\left[a_{i j}\right]=\left[\begin{array}{rrr}2 & 3 & -5 \\ 1 & 4 & 9 \\ 0 & 7 & -2\end{array}\right]$ and $B=\left[b_{i j}\right]=$ $\left[\begin{array}{cc}2 & -1 \\ -3 & 4 \\ 1 & 2\end{array}\right]$

then find (i) $a_{22}+b_{21}$

(ii) $a_{11} b_{11}+a_{22} b_{22}$

Solution:

(i)

$a_{22}+b_{21}$

Here,

$a_{22}=4$ and $b_{21}=-3$

$\Rightarrow a_{22}+b_{21}=4-3=1$

(ii)

$a_{11} b_{11}+a_{22} b_{22}$

Here,

$a_{11}=2, b_{11}=2, a_{22}=4$ and $b_{22}=4$

$\Rightarrow a_{11} b_{11}+a_{22} b_{22}=2 \times 2+4 \times 4$

$\Rightarrow a_{11} b_{11}+a_{22} b_{22}=4+16$

$\Rightarrow a_{11} b_{11}+a_{22} b_{22}=20$

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