Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET2011MathematicsDeterminants

The value of ^ a for which the system of equations array r a³ x+(a+1)³ y+(a+2)³ z=0 a x+(a+1) y+(a+2) z=0 x+y+z=0 array has a non-zero solution is

Options

  1. A1
  2. B0
  3. C-1
  4. DNone of these

Correct answer

C. -1

Step-by-step solution

For non-zero solution, | array ccc a³ & (a+1)³ & (a+2)³ a & (a+1) & (a+2) 1 & 1 & 1 array |=0 . array l - | array ccc 1 & 1 & 1 a & (a+1) & (a+2) a³ & (a+1)³ & (a+2)³ array |=0 & -(a-a-1)(a+1-a-2)(a+2-a) & (a+a+1+a+2)=0 & -2(3 a+3)=0 & a=-1 & [ array ccc 1 & 1 & 1 x & y & z x³ & y³ & z³ array = . (x-y)(y-z)(z-x)(x+y+z) array ]

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 MHT CET PYQs