If a > 0 and discriminant of ax^{2}+2bx+c is –ve, then
If the system of linear equations
x + 2ay +az = 0 ; x +3by+bz = 0 ; x +4cy+cz = 0 ; has a non  zero solution, then a, b, c.
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If 1, ω,ω^{2} are the cube roots of unity, then
The only correct statement about the matrix A is
If B is the inverseof matrix A, then α is
If a_{1}, a_{2} , a_{3}, ......,a_{n}, .... are in G.P., then the value of the determinant
If A^{2} – A +I=0 , then the inverse of A is
The system of equations
α x + y + z = α – 1
x + α y + z = α – 1
x + y + α z = α – 1
has infinite solutions, if α is
If a^{2} + b^{2 }+ c^{2} = – 2 and
then f (x) is a polynomial of degree
If a_{1} , a_{2},a_{3} , ............, an , ...... are in G. P., then the determinant
is equal to
If A and B are square matrices of size n × n such that A^{2}  B^{2} = (A B)(A+B), then which of the following will be always true?
Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr(A), the sum of diagonal entries of a. Assume that A^{2} = I.
Statement1 : If A ≠ I and A ≠ –I, then det(A) = –1
Statement2 : If A ≠ I and A ≠ –I, then tr (A) ≠ 0.
Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx, and z = bx + ay. Then a^{2} + b^{2} + c^{2} + 2abc is equal to
Let A be a square matrix all of whose entries are integers. Then which one of the following is true?
Let A be a 2 × 2 matrix
Statement 1 : adj (adj A) = A
Statement 2 : adj A = A
Let a, b, c be such that b(a + c) ≠ 0 if
then the value of n is :
The number of 3 × 3 nonsingular matrices, with four entries as 1 and all other entries as 0, is
Let A be a 2 × 2 matrix with nonzero entries and let A^{2} = I , where I is 2 × 2 identity matrix. Define Tr(A) = sum of diagonal elements of A and A = determinant of matrix A.
Statement  1 : Tr(A) = 0.
Statement 2 : A = 1.
Consider the system of linear equations ;
x_{1} + 2x_{2} + x_{3} = 3
2x_{1} + 3x_{2} + x_{3} = 3
3x_{1} + 5x_{2} + 2x_{3} = 1
The system has
The number of values of k for which the linear equations 4x + ky + 2z = 0 , kx + 4y + z = 0 and 2x + 2y + z = 0 possess a nonzero solution is
Let A and B be two symmetric matrices of order 3.
Statement1: A(BA) and (AB)A are symmetric matrices.
Statement2: AB is symmetric matrix if matrix multiplication of A with B is commutative.
If u_{1} and u_{2} are column matrices such that then u_{1} + u_{2} is equal to :
Let P and Q be 3 x 3 matrices P ≠ Q. If P^{3} = Q^{3} and P^{2}Q = Q^{2}P then determinant of (P^{2} + Q^{2}) is equal to :
If is the adjoint of a 3 × 3 matrix A and A = 4, then α is equal to :
If α, β ≠ 0, and f (n) = α^{n} +β^{n} and
then K is equal to:
If A is a 3 × 3 nonsingular matrix such that AA' = A'A and B = A^{–1}A', then BB' equals:
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209 videos443 docs143 tests
