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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

 

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