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  • Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 15 Subquestion (iii) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.2 Question 15 Subquestion (iii) Maths Textbook Solution.

Answers (1)

Answer: x = 1, y = 2
Hint: Solve LHS part and then equate with RHS part.
Given:

x \begin{bmatrix} 2\\1 \end{bmatrix} + y \begin{bmatrix} 3\\5 \end{bmatrix} +\begin{bmatrix} -8\\11 \end{bmatrix} = 0
Here, we have to compute x  and y .
Solution:

x \begin{bmatrix} 2\\1 \end{bmatrix} + y \begin{bmatrix} 3\\5 \end{bmatrix} +\begin{bmatrix} -8\\11 \end{bmatrix} = 0

\begin{bmatrix} 2x+3y-8\\x+5y-11 \end{bmatrix} = \begin{bmatrix} 0\\0 \end{bmatrix}

Equating this, we get:

2x+3y-8 = 0
\Rightarrow 2x+3y=8                                                                                      …(1)                                                                                  

Also,

x+5y-11 = 0
\Rightarrow x=11-5y                                                                                      …(2)                                                    
Applying the value of ‘x ’ in equation (1), we get:

2(11 -5y) + 3y = 8
22 -10y + 3y = 8
-7y = 8 -22
-7y = -14
y = 2

Applying the value of ‘y’ in equation (2), we get:

x = 11 - 5(2)
x = 11- 10
x = 1

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