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  • Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 21 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 21 Maths Textbook Solution.

Answers (1)

Answer: A= B

Given:
A= \begin{bmatrix} a+4 &3b \\ 8 &-6 \end{bmatrix},B\begin{bmatrix} 2a+2 &b^{2}+2 \\ 8 & b^{2}-10 \end{bmatrix}
We have to find out the value of a and b
Hint: We will use equality of matrices.
Solution:  
 A= \begin{bmatrix} a+4 &3b \\ 8 &-6 \end{bmatrix},B\begin{bmatrix} 2a+2 &b^{2}+2 \\ 8 & b^{2}-10 \end{bmatrix}

\because A= B 

Corresponding elements of two equal matrix are equal.

a+4= 2a+2                                                                                                                                      ….. (i)                   

 3b=b^{2}+2                                                                                                                                          ….. (ii)

 b^{2}-10= -6                                                                                                                                       ….. (iii)
Solving equation (i), We get

a+4=2a+2\\\Rightarrow 2a-a=4-2\\\Rightarrow a=2

Solving equation (ii), We get

b^{2}-3b+2=0\\\Rightarrow b^{2}-2b-b+2= 0\\\Rightarrow b\left ( b-2 \right )-1\left ( b-2 \right )= 0\\\Rightarrow \left ( b-1 \right )\left ( b-2 \right )= 0\\\Rightarrow = 1\: or\: 2

Solving equation (iii), We get

b^{2}-10= -6\\\Rightarrow b^{2}= -6+10\\\Rightarrow b^{2}= 4\\\Rightarrow b= \pm 2

Here, we have common value of b= 2 from equation (ii) and (iii)
Hence, a=2,b= 2

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