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  • need solution for RD Sharma maths class 12 chapter 5 Determinants exercise Fill in the blanks question 27

need solution for RD Sharma maths class 12 chapter 5 Determinants exercise Fill in the blanks question 27

Answers (1)

Answer: (y-z)(z-x)[y-x+x y z]

Hint: Here, we use basic concept of determinant of matrix

Given: \left[\begin{array}{ccc} 0 & x y z & x-z \\ y-x & 0 & y-z \\ z-x & z-y & 0 \end{array}\right]

Solution:             

                0\left[\begin{array}{cc} 0 & y-z \\ z-y & 0 \end{array}\right]-x y z\left[\begin{array}{cc} y-x & y-z \\ z-x & 0 \end{array}\right]+x-z\left[\begin{array}{cc} y-x & 0 \\ z-x & z-y \end{array}\right]

                \begin{aligned} &=0(0-(y-z)) \times(z-y)-x y z(0-(y-z)(z-x))+(x-z)((y-x)(z-y)-0) \\ &=x y z(y-z)(z-x)+(z-x)(y-z)(y-z) \\ &=(y-z)(z-x)[x y z+(y-x)] \\ &=(y-z)(z-x)[y-x+x y z] \end{aligned}

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