Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202120 Aug 2021Evening ShiftMathematicsDeterminantsActual

If x x 2 1 + x 3 y y 2 1 + y 3 z z 2 1 + z 3 = 0 and x , y , z are all distinct, then x y z =

Options

  1. A- 1
  2. B1
  3. C0
  4. D3

Correct answer

A. - 1

Step-by-step solution

Given, If x x 2 1 + x 3 y y 2 1 + y 3 z z 2 1 + z 3 = 0 x x 2 1 y y 2 1 z z 2 1 + x x 2 x 3 y y 2 y 3 z z 2 z 3 = 0 Taking x , y , z from C 1 , C 2 , C 3 respectively x x 2 1 y y 2 1 z z 2 1 + x y z 1 x x 2 1 y y 2 1 z z 2 = 0 By interchanging the columns twice x x 2 1 y y 2 1 z z 2 1 + x y z x x 2 1 y y 2 1 z z 2 1 = 0 x x 2 1 y y 2 1 z z 2 1 1 + x y z = 0 R 1 → R 1 - R 2   &   R 2 →   R 2 - R 3 x - y x 2 - y 2 1 - 1 y - z y 2 - z 2 1 - 1 z z 2 1 1 + x y z = 0 x - y x - y x + y 0 y -

Practice Determinants on Quantrex Academy →

More from Determinants

Let A = [a_ ij ] be a square matrix of order 3 3 , where the elements are defined as a_ ij = cases i - 2j & if i = j 0 & if i > j 1 & if i < j cases then the value of |A^t| is 2026Let A be a square matrix of order 3 3 . If |A| = -4 , then the value of | A⁻¹ -2 | is: 2026Given P = bmatrix 2 & & 1 1 & 2 & 2 1 & 3 & 3 bmatrix is the adjoint of a 3 3 matrix A and |A| = 3 , then the value of is: 2026Which of the following is correct? 2026If A and B are invertible square matrices of order n, then which of the following is not correct? 2026The system of equations x + 2y = 3 and 2x + 3y = 3 has 2026A value of lying between 0 and 2 and satisfying | array ccc 1+ ^2 & ^2 & 4 4 ^2 & 1+ ^2 & 4 4 ^2 & ^2 & 1+4 4 array |=0 2025If the inverse of [ array ccc -x & 14 x & 7 x 0 & 1 & 0 x & -4 x & -2 x array ] is [ array ccc 2 & 0 & 7 0 & 1 & 0 1 & -2 & 1 array ] , then | array ccc x & x+1 & x+2 x+1 & x+2 & x 2025 Full Determinants list All AP EAMCET PYQs