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  • Provide Solution For R. D. Sharma Maths Class 12 Chapter 5.2 determinants Exercise MCQs Question 2 sub question 11 Maths Textbook Solution.

Provide Solution For  R. D. Sharma Maths Class 12 Chapter 5.2 determinants Exercise MCQs Question 2 sub question 11 Maths Textbook Solution.

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Answer:\left|\begin{array}{ccc} a & b & c \\ a+2 x & b+2 y & c+2 z \\ x & y & z \end{array}\right|=0

Hint: We will try to do any two column or row equal

Given:\left|\begin{array}{ccc} a & b & c \\ a+2 x & b+2 y & c+2 z \\ x & y & z \end{array}\right|

Solution:\left|\begin{array}{ccc} a & b & c \\ a+2 x & b+2 y & c+2 z \\ x & y & z \end{array}\right|

\begin{aligned} &\text { Applying } R_{3} \rightarrow 2 \times R_{3}+R_{1} \\ &\left|\begin{array}{ccc} a & b & c \\ a+2 x & b+2 y & c+2 z \\ 2 x+a & 2 y+b & 2 z+c \end{array}\right| \end{aligned}

If any two rows or columns of a determinant are identical.

The value of the determinant is zero

=0 \quad\left(\because R_{2}=R_{3}\right)

Hence \left|\begin{array}{ccc} a & b & c \\ a+2 x & b+2 y & c+2 z \\ x & y & z \end{array}\right|=0

 

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