Test: Matrices & Determinants - 5 - Mathematics MCQ

If the system of equations x - ky - z = 0, kx - y - z = 0, x + y - z = 0 has a non-zero solution, then the possible values of k are

The number of distinct real roots of in the intervalis

If for a triangle ABC,  then what is the value of sin³ A + sin³ B + sin³ C?

If the system of equations x - Ky - z = 0, Kx - y - z = 0 and x + y - z = 0 has a non-zero solution, then the possible values of K are

If a > 0 and discriminant of ax² + 2bx + c is negative, then

If A is an invertible matrix and B is a matrix, then

If every minor of order r of a matrix A is zero, then rank of A is

The system of equations kx + y + z = 1, x + ky + z = k and x + y + kz = k2 have no solution if k equals

For what value of λ, the system of equations x - 2y + z = 0, 2x - y + 3z = 0, x + y - z = 0 has the trivial solution as the only solution.

If x ≠ y ≠ z and then xyz is equal to

For a₁ ≠ 0 (I = 1, 2, 3, ……., n) the sum of co-factors of all elements of the determinant for all n is

The system of equations x + 2y - z = 3, 2x - 2y + 3z = 2, 3x - y + 2z = 1 has

If = 0 and x ≠ 0, then

The determinant= 

The value of 

The system of equations - 2x + y + z = a, x - 2y + z = b, x + y - 2z = c has no solution, if

If  d(r)  is equal to