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  • Provide solution for RD Sharma maths Class 12 Chapter 5 Determinants Exercise VSQ Question 51 maths textbook solution.

Provide solution for RD Sharma maths Class 12 Chapter 5 Determinants Exercise VSQ Question 51 maths textbook solution.

Answers (1)

Answer:0

Hint: Here we use basic concept of determinant of matrix

Given: \left|\begin{array}{ccc} x+y & y+z & z+x \\ z & x & y \\ -3 & -3 & -3 \end{array}\right|

Solution :

\rightarrow Let's perform row operations

\begin{aligned} &\mathrm{R}_{1} \rightarrow \mathrm{R}_{1}+\mathrm{R}_{2} \\ &=\left|\begin{array}{ccc} x+y+z & x+y+z & x+y+z \\ z & x & y \\ -3 & -3 & -3 \end{array}\right| \end{aligned}

\rightarrow Let's take (x+y+z) common from R_{1} and -3 from R_{3}

=(x+y+z)(-3)\left|\begin{array}{lll} 1 & 1 & 1 \\ z & x & y \\ 1 & 1 & 1 \end{array}\right|

\rightarrow Here we exan clearly see that two rows are identical.

So, it's determinate is 0.

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