#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 17 Maths Textbook Solution.

Answer:$\lambda = 2$

Hint: Add LHS part of matrix and separate the variable $\lambda$ .Then, solve.

Given:$\lambda \begin{bmatrix} 1 & 0 &2 \\ 3 & 4 & 5 \end{bmatrix} +2 \begin{bmatrix} 1 & 2 & 3\\ -1 & -3 & 2 \end{bmatrix} = \begin{bmatrix} 4 & 4 &10 \\ 4 & 2 & 14 \end{bmatrix}$

Here, we have to find the value of $\lambda$

Solution:

$\lambda \begin{bmatrix} 1 & 0 &2 \\ 3 & 4 & 5 \end{bmatrix} +2 \begin{bmatrix} 1 & 2 & 3\\ -1 & -3 & 2 \end{bmatrix} = \begin{bmatrix} 4 & 4 &10 \\ 4 & 2 & 14 \end{bmatrix}$

$\lambda \begin{bmatrix} \lambda & 0 &2\lambda \\ 3\lambda & 4\lambda & 5\lambda \end{bmatrix} +2 \begin{bmatrix} 1 & 2 & 3\\ -1 & -3 & 2 \end{bmatrix} = \begin{bmatrix} 4 & 4 &10 \\ 4 & 2 & 14 \end{bmatrix}$

$\lambda \begin{bmatrix} \lambda+2 & 0+4 &2\lambda +6 \\ 3\lambda -2 & 4\lambda -6 & 5\lambda +4 \end{bmatrix} = \begin{bmatrix} 4 & 4 &10 \\ 4 & 2 & 14 \end{bmatrix}$
Equating this, we get:

$\lambda +2 = 4$

$\lambda = 4 - 2$

$\Rightarrow \lambda = 2$