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Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 10 Maths Textbook Solution.

Answers (1)

Answer:    a= 1,b=2,c=3,d=4   

Given: \begin{bmatrix} 2a+b &a-2b\\ 5c-d &4c+3d \end{bmatrix}= \begin{bmatrix} 4 &-3\\ 11&24 \end{bmatrix}

Here we have to find out the values of  a,b,c  and d.

Hint: If two matrices are equal then the elements of each matrix are also equal.


Given that two matrices are equal

\therefore  By equating them, we get

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

               a-2b=-3                                                                                                                                   ……(ii)

               5c-d=11                                                                                                                                    ……(iii)

and        4c+3d=24                                                                                                                                ……(iv)

Multiplying eqn(i) by 2 and adding to eqn(ii) we get


\Rightarrow 5a=5

\Rightarrow a=1

Now, substituting the value of a in eqn(i)

2\times 1+b=4

\Rightarrow b=4-2

\Rightarrow b=2

Multiplying eqn(iii) by 3 and adding to eqn(iv) we get

15c-3d+4c+3d=33+24\\\\\Rightarrow 19c=57\\\\\Rightarrow c=3

Now, substituting the value of c in eqn(iv) we get

4\times 3+3d=24\\\\\Rightarrow 12+3d=24\\\\\Rightarrow 3d=24-12\\\\\Rightarrow d=\frac{12}{3}\\\\\Rightarrow d=4

Hence   a= 1,b=2,c=3,d=4

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