Question

If A = [a_ij] =`[[2,3,-5],[1,4,9],[0,7,-2]]`and B = [b_ij] `[[2,-1],[-3,4],[1,2]]`

then find (i) a₂₂ + b₂₁ (ii) a₁₁ b₁₁ + a₂₂ b₂₂

 

 

Answer 1

\[\left( i \right)\]\[a_{22} + b_{21}\]\[\]
\[Here, \]
\[ a_{22} =4\text{ and }b _{21}= - 3 \]

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

\[\left ( ii \right)\]
\[\]\[a_{11} b_{11} + a_{22} b_{22}\]

here 
`a_11=2,   b_11=2,a_22=4` and `b_22=4`\[ \Rightarrow a_{11} b_{11} + a_{22} b_{22} = 2 \times 2 + 4 \times 4\]
\[ \Rightarrow a_{11} b_{11} + a_{22} b_{22} = 4 + 16\]
\[ \Rightarrow a_{11} b_{11} + a_{22} b_{22} = 20\]