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

If A = ( array ccc 1 & 5 & 3 2 & 4 & 0 3 & -1 & -5 array ), B = ( array c -1 -2 4 array ) and [ x y z ] A ^ T = B ^ T , then x+y+z=

Options

  1. A4
  2. B-2
  3. C6
  4. D3

Correct answer

C. 6

Step-by-step solution

aligned & [ array ll x y z array ] [ array ccc 1 & 2 & 3 5 & 4 & -1 3 & 0 & -5 array ]= [ array lll -1 & -24 array ] & [x+5 y+3 z 2 x+4 y 3 x-y-5 z]= [ array lll -1 & -2 & 4 array ] aligned x+5 y+3 z=-1 ...(i) 2 x+4 y=-2, x+2 y=-1 ...(ii) 3 x-y-5 z=4 ...(iii) Solving eqs. (i), (ii) & (iii), we get x=6, y=-7 / 2, z=7 / 2 x+y+z=6- 7 2 + 7 2 =6

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