Linear Transform MCQ - 1 - Mathematics MCQ

Let T:R² -> R² be the transformation T(x₁,x₂) = (x₁,0). The null space (or kernel) N(T) of T is

defined by differentiation and integration 

Which of the following is not linear?

be the vector space of all complex numbers over complex field be defined by T(z) =

Given then find a + b.

Let T:  R³ → R³ be a linear transformation and I be the identify transformation of  R3. If there is a scalar C and a non-zero vector x ∈ R³ such that T(x) = Cx, then rank (T – CI) 

Which of the following Linear Transformations is not correct for the given matrix?

Find the inverse Fourier transform of

Consider the basis S = {v₁, v₂, v₃} for where v₁ = (1,1,1) and v₂ = (1,1,0), v₃ = (1,0,0) and let  be a linear transformation such that T(v₁) = (1,0), T (v₂) = (2, -1), T (v₃) = (4, 3). Then T (2, - 3, 5) is

Which one of the following is not a criterion for linearity of an equation? 

Consider the following  such that T(2,2) = (8, - 6), T (5, 5) = (3, - 2) Then

Let T be linear transformation on  into itself such that T(1,0) = (1,2) and T (1, 1) = (0, 2) .Then T(a, b) is equal to

Which of the following mapping   is not a linear mapping?

If is given by T (x, y, z) = (x - y, y + 3z, x + 2y). Then T^-1 is

Find the sum of the Eigen values of the matrix

Let T: R³ → R³ be a linear transformation and I be the identity transformation of R³. If there is a scalar C and a non-zero vector x ∈ R³ such that T(x) = Cx, then rank (T – CI)

where T be the reflection of the points through the line y = -x then the matrix of T with respect to standard basis is

Consider the two linear mapsT₁ and T₂ on V₃ defined as T₁(x₁, x₂, x₃) = (0, x₂, x₃) and T₂(x₁, x₂, x₃) = (x₁, 0,0)

Let T be a linear transformation on the vector space defined by T(a, b) = (a, 0) the matrix of T relative to the ordered basis {(1,0), (0,1)} of is

Let A be an n × n matrix such that the set of all its nonzero eigenvalues has exactly r elements. Which of the following statements is true?

Let be the polynomial space with basis {1, x, x²} then matrix representation of  

Find the fourier transform of F(x) = 1, |x| < a0, otherwise.

Let be defined by T(p(x)) = p"(x) + p'(x). Then the matrix representation of T with respect to basis {1, x, x², x³} and {1, x, x²} of and  respectively is

For the standard basis {(1,0,0), (0,1,0), (0,0,1)} of is a linear transformation T from has the matrix representation Then the image of (2,1,2) under T is

Let us consider a 3×3 matrix A with Eigen values of λ₁, λ₂, λ₃ and the Eigen values of A^-1 are?

Let  be the map given by  If the matrix of T relative to the standard basis β = γ = {1, x, x², x³} is

A linear transformation T rotates each vector in clockwise through 90°. The matrix T relative to standard ordered basis