Linear Transform MCQ - 3 - IIT JAM MCQ

If a eigenvalue of A is λ, then the corresponding eigen value of A⁻¹ is

Let  where T be the reflection of the points through the line y = - x then

Let T be a linear operator on a finite dimensional vector space V. If m(λ) = λ^r + a_r-1λ^r-1 + ..... + a₀λ be a minimal polynomial of T then 

Let T be a linear operator on a finite dimensional space V and C is any scalar then C is characteristic value of T if

Let   be an linear operator having n distinct eigenvalues. Then

Let V is an n-dimensional vector space over the field the characteristic polynomial of the identity operator on V is

Let V be a finite dimensional vector space over the field the minimal polynomial for the zero operator is

Let    such that T(x₁, x₂, ...., x_n) = (0, x₁, x₂, ..... x_{n - 1}) then

If T be a linear operator on a vector space V such that T² - T + 1 = 0 then

If T : V → V be a linear operator for dim V = n and T has n distinct eigenvalues then

Let A and B he nxn matrices with the same minimal polynomial. Then

Let be defined by T(x, y, z) = (x + y + z, -x - y, -x - z) and M be its matrix with respect to standard ordered basis. The matrix M is similar to a matrix which is

A matrix M has eigenvalue 1 and 4 with corresponding eigenvectors (1, -1)^T and (2,1)^T respectively. Then M is

Let V be vector space of real polynomials of degree atmost 2. Define a linear operator  the dimension of the eigenspace of T^-1 corresponding to the eigenvalue 1 is 

Let A be an n x n matrix from the set of numbers and A³ - 3A² + 4A - 6I = 0 where I is n x n unit matrix. If A^-1 exists then 

Let A be n x n matrix which is both Hermitian and unitary, then 

The characteristic polynomial of the 3 x 3 real matrix 

Which of the following statement is correct?

if P is modal matrix for A then P^-1 AP is

Let A be 3 x 3 matrix with real entries such that det(A) = 6 and the trace of A is 0. lf det(A + I) = 0 where I denotes the 3 x 3 identity matrix, then the eigenvalues of A are

The eigenvalue of the matrix 

It the characteristic root of  are λ₁ and A₂, the characteristic roots of 

A is any nxn matrix with all entries equal to 1 then 0 is an eigenvalue of A and

 which of the follow ing is the zero matrix.

Consider the matrix  where a, b and c are non zero real numbers.Then the matrix has

Let the characteristic equation of a matrix (x - α)³ + (x - β)³ a be λ² - λ - 1 then