Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202318 May 2023Evening ShiftMathematicsMatricesActual

The sum of the distinct values of x for which the matrix A= [ array lll 1 & 1 & x 1 & x & 1 x & 1 & 1 array ] has no inverse, is

Options

  1. A4
  2. B3
  3. C2
  4. D-1

Correct answer

D. -1

Step-by-step solution

If matrix A has no inverse, then det ( A )=0 aligned & | array ccc 1 & 1 & x 1 & x & 1 x & 1 & 1 array |=0 & x^3-3 x+2=0 & x^2(x-1)+x(x-1)-2(x-1)=0 & (x-1)(x+2)(x-1)=0 & (x-1)^2(x+2)=0 x=-2,+1,+1 aligned Sum of distinct values of x=-2+1=-1 .

Practice Matrices on Quantrex Academy →

More from Matrices

Given A = bmatrix x & 1 & -2 bmatrix and B = bmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 bmatrix . If ABA^t = [-20] then the value of x is: 2026If the matrix M = bmatrix x+5 & a & -4 -2 & 0 & b c & 6 & y+1 bmatrix is a skew symmetric matrix, the value of the expression ab + c^2 - xy is: 2026Matrix A = bmatrix 1 & 1 & 2 1 & -2 & 2 1 & 0 & -1 bmatrix , Given M₂₂ and A₃₂ are the minor and cofactor of the adjoint matrix of A respectively then the value of the expression M 2026If A and B are two square matrices of the same order such that AB = A and BA = B , then (A + B)^2 is equal to: 2026Given the matrices A = bmatrix 1 & 0 & 1 0 & 1 & 0 1 & 0 & 2 bmatrix and B = bmatrix 2 & 1 & 0 1 & 1 & 2 0 & 2 & 1 bmatrix , then the minor M₂₃ of the matrix (A B⁻¹)⁻¹ is: 2026Given A = pmatrix 1 & 2 2 & 3 pmatrix and f(x) = x^2 - 2x - 3 then f(A) is: 2026If the system of equations 2 x+p y+6 z=8, x+2 y+q z=5 and x+y+3 z=4 has infinitely many solutions, then p = 2025If x^a y^b=e^m, x^c y^d=e^n, ₁= | array ll m & b n & d array |, ₂= | array ll a & m c & n array |, ₃= | array ll a & b c & d array | , then the values of x and y are respectively ( 2025 Full Matrices list All AP EAMCET PYQs