Determinants questions
307 published questions with worked solutions.
- Let A = bmatrix 2 & b & 1 b & b^2 + 1 & b 1 & b & 2 bmatrix where b > 0. Then the minimum value of (A) b is:
- The number of values of θ ∈ (0, π) for which the system of linear equations x + 3y + 7z = 0, −x + 4y + 7z = 0, (sin 3θ)x + (cos...
- Let d ∈ R, and A = bmatrix -2 & 4 + d & ( ) - 2 1 & ( ) + 2 & d 5 & (2 ) - d & (- ) + 2 + 2d bmatrix , θ ∈ [0, 2π]. If the...
- If the system of linear equations, x+y+z=6 x+2y+3z=10 3x+2y+ z= has more than two solutions, then - ^2 is equal to_________.
- Let a – 2b + c = 1. If f(x)= vmatrix x+a & x+2 & x+1 x+b & x+3 & x+2 x+c & x+4 & x+3 vmatrix , then -
- If for some and in R, the intersection of the following three planes x + 4y - 2z = 1 x + 7y - 5z = x + 5y + z = 5 is a line in...
- If A = bmatrix 2 & 1 -1 & 2 bmatrix , B = bmatrix 1 & 0 1 & 1 bmatrix , C = ABA^T and X = A^TC^2A, then det X is equal to:
- If the system of equations x + (√2 sin α)y + (√2 cos α)z = 0, x + (cos α)y + (sin α)z = 0, x + (sin α)y − (cos α)z = 0 has a...
- Let α ∈ (0, ∞) and A = bmatrix 1 & 2 & 1 & 0 & 1 0 & 1 & 2 bmatrix . If det(adj(2A − Aᵀ) · adj(A − 2Aᵀ)) = 2⁸, then (det(A))² is...
- Let A be a 3 × 3 matrix of non-negative real elements such that A bmatrix 1 1 1 bmatrix = 3 bmatrix 1 1 1 bmatrix . Then the...
- If the system of equations 11x + y + λz = −5, 2x + 3y + 5z = 3, 8x − 19y − 39z = μ has infinitely many solutions, then λ⁴ − μ is...
- Let αβ ≠ 0 and A = bmatrix & & 3 & & - & & 2 bmatrix . If B = bmatrix 3 & -9 & 3 - & 7 & -2 -2 & 5 & -2 bmatrix is the matrix of...
- For α, β ∈ R and a natural number n, let A_r = vmatrix r & 1 & n^2 2 + 2r & 2 & n^2 - 3r - 2 & 3 & n(3n - 1) 2 vmatrix . Then...
- If the system of linear equations 2x+2ay+az=0, 2x+3by+bz=0, 2x+4cy+cz=0 Where a, b, c R are non-zero and distinct; has a non-zero...
- The system of linear equations x+2y+2z=5 2 x+3y+5z=8 4x+ y+6z=10 has :
- If the system of equations 2x + 7y + λz = 3, 3x + 2y + 5z = 4, x + μy + 32z = −1 has infinitely many solutions, then (λ − μ) is...
- Let A be a 2 × 2 real matrix with entries from 0, 1 and |A| ≠ 0. Consider the following two statements : (P) If A ≠ I_2, then |A|...
- If = vmatrix x-2&2x-3&3x-4 2x-3&3x-4&4x-5 3x-5&5x-8&10x-17 vmatrix =Ax^3+Bx^2+Cx+D, then B + C is equal to-
- Suppose the vectors x_1, x_2 and x_3 are the solutions of the system of linear equations, Ax = b when the vector b on the right...
- Let R. The system of linear equations 2x_1-4x_2+ x_3=1 x_1-6x_2+x_3=2 x_1-10x_2+4x_3=3 is inconsistent for :
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