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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.

Solution:

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

$4a+2b+a-2b=8-3$

$\Rightarrow 5a=5$

$\Rightarrow a=1$

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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