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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter determinants Exercise 5.2 Question 55 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter  determinants Exercise 5.2 Question 55 Maths Textbook Solution.

Answers (1)

Answer: 9(3 x y z+x y+y z+z x)

Hint: Use determinant formula

Given: \left|\begin{array}{ccc} 1 & 1 & 1+3 x \\ 1+3 y & 1 & 1 \\ 1 & 1+3 z & 1 \end{array}\right|=9(3 x y z+x y+y z+z x)

Solution:

\begin{aligned} &\text { L.H.S }\left|\begin{array}{ccc} 1 & 1 & 1+3 x \\ 1+3 y & 1 & 1 \\ 1 & 1+3 z & 1 \end{array}\right| \\ &\text { Apply } \mathrm{R}_{1} \rightarrow R_{1}-R_{3} \& R_{2} \rightarrow R_{2}-R_{3} \\ &\left|\begin{array}{ccc} 0 & -3 z & 3 x \\ 3 y & -3 z & 0 \\ 1 & 1+3 z & 1 \end{array}\right| \end{aligned}

\begin{aligned} &3 \text { common from } \mathrm{R}_{1} \& R_{2}\\ &3 \times 3\left|\begin{array}{ccc} 0 & -z & x \\ y & -z & 0 \\ 1 & 1+3 z & 1 \end{array}\right| \end{aligned}

\begin{aligned} &\text { Expand from } \mathrm{R}_{1}\\ &9[z(y)+x(y+3 z y+z)\\ &9(3 x y z+x y+y z+z x) \end{aligned}

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