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Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 2 Subquestion (i) Maths Textbook Solution.

Answers (1)

Answer: $20$
Given: Here given that
$A= \left [ a_{ij} \right ]= \begin{bmatrix} 2 & 3 &-5 \\ 1& 4 & 9 \\ 0& 7 &-2 \end{bmatrix}$    and    $B= \left [ b_{ij} \right ]= \begin{bmatrix} 2 &-1 \\ -3& 4\\ 1& 2 \end{bmatrix}$
Here we have to find out the values of $a_{11}b_{11}+a_{22}b_{22}= 1$
Hint: Simply we select the elements in the matrix which elements required and simplify
Solution: We know that
$A= \left [ a_{ij} \right ]= \begin{bmatrix} a_{11} &a_{12} &a_{13} \\ a_{21} & a_{22} & a_{23}\\ a_{31}& a_{32} & a_{33} \end{bmatrix}$                    $\cdot \cdot \cdot \left ( i \right )$
$B= \left [ b_{ij} \right ]= \begin{bmatrix} b_{11} &b_{12} \\ a_{21} & a_{22} \\ a_{31}& a_{32} \end{bmatrix}$                     $\cdot \cdot \cdot \left ( ii \right )$
Also given that
$A= \left [ a_{ij} \right ]= \begin{bmatrix} 2 & 3 &-5 \\ 1& 4 & 9 \\ 0& 7 &-2 \end{bmatrix}$        and    $B= \left [ b_{ij} \right ]= \begin{bmatrix} 2 &-1 \\ -3& 4\\ 1& 2 \end{bmatrix}$
Now comparing with eqn(i) and (ii) we have,
$a_{11}= 2$              $a_{22}= 4$
$b_{11}= 2$                 $b_{22}= 4$
Hence, $a_{11}b_{11}+a_{22}b_{22}= 2\times 2+4\times 4$
                                          $= 4+16$
$a_{11}b_{11}+a_{22}b_{22}= 20$