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

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

Answers (1)

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

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