Description

This mock test of Linear Transform MCQ - 1 for Mathematics helps you for every Mathematics entrance exam.
This contains 30 Multiple Choice Questions for Mathematics Linear Transform MCQ - 1 (mcq) to study with solutions a complete question bank.
The solved questions answers in this Linear Transform MCQ - 1 quiz give you a good mix of easy questions and tough questions. Mathematics
students definitely take this Linear Transform MCQ - 1 exercise for a better result in the exam. You can find other Linear Transform MCQ - 1 extra questions,
long questions & short questions for Mathematics on EduRev as well by searching above.

QUESTION: 1

The unique linear transformation such that T(1,2) = (2,3) and T(0,1) = (1,4). Then H rule for T is

Solution:

QUESTION: 2

Let V and W be vector spaces over be a map. Then T is a linear transformation iff

Solution:

QUESTION: 3

is a linear transformation T(1,0) = (2,3,l) and T(1,1) = (3,0,2) then which one of the following statement is correct?

Solution:

QUESTION: 4

Let T:R^{2} -> R^{2} be the transformation T(x_{1},x_{2}) = (x_{1},0). The null space (or kernel) N(T) of T is

Solution:

QUESTION: 5

defined by differentiation and integration

Solution:

QUESTION: 6

Which of the following is not linear?

Solution:

QUESTION: 7

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

Solution:

QUESTION: 8

Consider the vector space and the maps defined by f(x,y,z) = (x, |y|,z) and g(x,y,z) = (x + 1,y - 1, z).Then

Solution:

QUESTION: 9

be the linear transformation given by T(x,y, z) = (x,y) with respect to standard basis of and the basis {(0,1). (1,1)} of What is the matrix representation of T?

Solution:

QUESTION: 10

Define T on into it self by T(x_{1}, x_{2}) = (x_{1} + x_{2}, x_{1} - x_{2}).Then matrix of T^{-1} relative to the standard basis for

Solution:

QUESTION: 11

Which of the following is a linear transformation from

(I)

(II)

(III)

Solution:

QUESTION: 12

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

Solution:

QUESTION: 13

is set of real numbers in let f_{1} and f_{2} be the two transformation defined by f_{1}(x,y) = (0,y), f_{2}(x,y) = (y,x). Then the product of the mapping (f_{2} _{°} f_{1})(x,y) gives the projection of the x - y plane on the

Solution:

QUESTION: 14

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

Solution:

QUESTION: 15

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

Solution:

QUESTION: 16

Which of the following mapping is not a linear mapping?

Solution:

QUESTION: 17

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

Solution:

QUESTION: 18

Let be the vector space of all polynomials over of degree less than or equal to 2. Let D be the differential operator on . Then m atrix of D relative to the basis (x^{2}, 1,x} is equal to

Solution:

QUESTION: 19

The matrix of the linear tranformation T on defined as T(x,y,z) = (2y + z, x - 4y, 3x) with respect to the basis β = {(1,1,1), (1,1,0), (1,0,0)} is

Solution:

QUESTION: 20

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

Solution:

QUESTION: 21

Consider the two linear mapsT_{1} and T_{2} on V_{3} defined as T_{1}(x_{1}, x_{2}, x_{3}) = (0, x_{2}, x_{3}) and T_{2}(x_{1}, x_{2}, x_{3}) = (x_{1}, 0,0)

Solution:

QUESTION: 22

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

Solution:

QUESTION: 23

Let W be the vector space of all real polynomials of degree atmost 3. Define T : W → W by T(p(x)) = p'(x) where p'(x) is the derivative of P.The matrix of T in the basis {1, x, x^{2}, x^{3}} considered as column vector is given by

Solution:

QUESTION: 24

Let be the polynomial space with basis {1, x, x^{2}} then matrix representation of

Solution:

QUESTION: 25

Let be a linear transformation defined by T(x, y, z) = (x + y - z, x + z, y - z) then the matrix of the linear transformation T with respect to ordered basis β = {(0,1,0), (0,0,1), (1,0,0)} of is

Solution:

QUESTION: 26

Let be defined by T(p(x)) = p"(x) + p'(x). Then the matrix representation of T with respect to basis {1, x, x^{2}, x^{3}} and {1, x, x^{2}} of and respectively is

Solution:

QUESTION: 27

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

Solution:

QUESTION: 28

be the vector space of all real polynomials of degree atmost 3. Define then the matrix of S in the basis {1,x,x^{2},x^{3}}. Considered as column vector is given by

Solution:

QUESTION: 29

Let be the map given by If the matrix of T relative to the standard basis β = γ = {1, x, x^{2}, x^{3}} is

Solution:

QUESTION: 30

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

Solution:

### Laplace Transform (Part - 1)

Video | 08:02 min

### Laplace Transform (Part -1)

Video | 53:44 min

### Laplace Transform (Part - 1)

Video | 08:02 min

### MCQ''s - Linear Harmonic Oscillator - I

Doc | 2 Pages

- Linear Transform MCQ - 1
Test | 30 questions | 90 min

- Linear Transform MCQ - 5
Test | 20 questions | 60 min

- Linear Transform MCQ - 3
Test | 30 questions | 90 min

- Linear Transform MCQ - 4
Test | 20 questions | 90 min

- Linear Transform MCQ - 2
Test | 30 questions | 90 min