Determinants questions
307 published questions with worked solutions.
- If S is the set of distinct values of 'b' for which the following system of linear equations x + y + z = 1 x + ay + z = 1 ax + by...
- If vmatrix x-4 & 2x & 2x 2x & x-4 & 2x 2x & 2x & x-4 vmatrix = (A + Bx)(x - A)^2, then the ordered pair (A, B) is equal to :
- If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z) then xz y^2...
- The number of values of k for which the system of linear equations, (k + 2)x + 10y = k, kx + (k + 3)y = k - 1 has no solution, is...
- The greatest value of c ∈ R for which the system of linear equations x - cy - cz = 0, cx - y + cz = 0, cx + cy - z = 0 has a...
- Let the numbers 2, b, c be in an A.P. and A = bmatrix 1 & 1 & 1 2 & b & c 4 & b^2 & c^2 bmatrix . If det(A) ∈ [2, 16], then c...
- Let λ be a real number for which the system of linear equations x + y + z = 6, 4x + y - z = - 2, 3x + 2y - 4z = -5 has infinitely...
- The sum of the real roots of the equation vmatrix x & -6 & -1 2 & -3x & x-3 -3 & 2x & x+2 vmatrix = 0, is equal to:
- If f(x) = vmatrix x & x & 1 2 x & x^2 & 2x x & x & 1 vmatrix , then _ x 0 f'(x) x
- Let S be the set of all real values of k for which the system of linear equations x + y + z = 2 2x + y - z = 3 3x + 2y + kz = 4...
- If the system of linear equations x + ay + z = 3 x + 2y + 2z = 6 x + 5y + 3z = b has no solution, then
- If _1 = vmatrix x & & - & -x & 1 & 1 & x vmatrix and _2 = vmatrix x & 2 & 2 - 2 & -x & 1 2 & 1 & x vmatrix , x ≠ 0; then for all...
- The system of linear equations x + y + z = 2, 2x + 3y + 2z = 5, 2x + 3y + (a^2 - 1)z = a + 1
- If A = bmatrix 1 & & 1 - & 1 & -1 & - & 1 bmatrix ; then for all ( 3 4 , 5 4 ), det(A) lies in the interval:
- The set of all values of λ for which the system of linear equations x − 2y − 2z = λx, x + 2y + z = λy, −x − y = λz has a...
- An ordered pair (α, β) for which the system of linear equations (1 + α)x + βy + z = 2, αx + (1 + β)y + z = 3, αx + βy + 2z = 2...
- If vmatrix a - b - c & 2a & 2a 2b & b - c - a & 2b 2c & 2c & c - a - b vmatrix = (a + b + c)(x + a + b + c)^2, x ≠ 0 and a + b +...
- Let A and B be two invertible matrices of order 3 × 3. If det(ABA^T) = 8 and det(AB^ -1 ) = 8, then det(BA^ -1 B^T) is equal to:
- If the system of linear equations 2x + 2y + 3z = a, 3x − y + 5z = b, x − 3y + 2z = c where a, b, c are non zero real numbers, has...
- Let a_1, a_2, a_3, , a_ 10 be in G.P. with a_i > 0 for i = 1, 2, …, 10 and S be the set of pairs (r, k), r, k ∈ N (the set of...
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