Let P4 = set of polynomials with degree less than or equal to 4, and T: P4 → P4 f → f′ (derived), ie T(f)=f′. Judge the following statements as true or false (a) The subset of P4 defined by N = {T ∈ P4 | T(p(x)) = 0} is a vector subspace of P4. (b) T is not a linear transformation.

Let P4 = set of polynomials with degree less than or equal to 4, and T: P4 → P4 f → f′ (derived), ie T(f)=f′. Judge the following statements as true or false (a) The subset of P4 defined by N = {T ∈ P4 | T(p(x)) = 0} is a vector subspace of P4. (b) T is not a linear transformation.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Suppose that F: R² → R² is an invertible linear transformation such that P(1)-(3) F and 28 P(1)-(2)…

A: If F: U→V be an Inverse Linear Transformation such that F(F-1(u)) =F-1(F(u)) = u…

Q: Determine whether T is a linear transformation. T: F --->R defined by T(f) = f( c),…

Q: Let V₁, V2, and v3 be vectors in a vector space V, and let T:V→ R³ be a linear transformation for…

Q: 11. Describe, in words, the transforming effect of the matrix representation of the linear…

A: Given that the matrix A=0110 is the matrix representation of the linear transformation R2→R2. Since…

Q: Show that the transformation T defined by T(x₁, x₂) = (4x₁2x₂, X₁ +3, 5x₂) is not linear. 0 If T is…

Q: Let T: R² R² be a linear transformation that sends the vector u = (5,2) into (2, 1) and maps v = (1,…

Q: Let T : ℝ² → ℝ² be a linear transformation defined by T(x, y) = (3x - 2y, x + 4y). Find the image of…

A: In this problem, we are given a linear transformation T which acts on vectors in R2 (2-dimensional…

Q: Let P, denote the vector space of polynomials in the variable of degree n or less with real…

Q: Let V denote the vector space of 2 x 2 matrices, and W the vector space of 3 x 2 matrices. Define…

A: It is given that, Tabcd=a+b2d2b-d-3c2b-c-3a

Q: Let Pn be the vector space of polynomials of degree at most n together with the zero polynomial.…

A: Given that Pn be the vector space of polynomials for degree at most n with the zero polynomial.…

Q: Given: region R below bounded by the graphs of (y – 2)² = x – 1, y = 3x – 11, and y = 1. (5, 4) (1,…

Q: Let P, denote the vector space of polynomials in the variable of degree or less with real…

Q: Let C1,2 be the vector space of continuous functions mapping the interval 1 <x<2 into R. Let T:…

Q: Let V₁, V2, and v3 be vectors in a vector space V, and let T:V→ R³ be a linear transformation for…

Q: Show that the transformation T defined by T(x₁, x₂) = (4x₁2x₂, X₁ +3, 5x₂) is not linear. If T is a…

Q: be the vector space of all polynomials of degree 3 or less in the variable z. Let PI(T) 2+x+1²,…

A: In this question, we check the given set forms a basis or not. Then we use elementary transformation…

Q: Let S and T be the linear transformations defined in R3 and a1 , a2 , a3 be the standard unit…

Q: Let T be the linear transformation from the space of degree three or less polynomials to itself…

A: Step 1Step 2 Step 3 Step 4

Q: M2x2 by T(A) = 3AT| transformation from the vector space M2x2to M2×2· Define the function T : M2x2…

Q: Let V₁, V2, and v3 be vectors in a vector space V, and let T:V → R³ be a linear transformation for…

Q: Let V be a vector space and let v, v2, vz e V. Suppose f : V → R³ is a linear transformation and fG)…

A: Given: f:V→ℝ3 is a linear transformation fv1=-5-45, fv2=-4-4-2, fv3=-12-4 a. As f is a linear…

Q: Let Pn denote the vector space of polynomials in the variable æ of degree n or less with real…

Q: Suppose H is a n-dimensional subspace. Let A = Let T H H be a linear transformation. Then [T] =…

Q: Let W be the subspace of R4 defined by the equation x₁ - x₂ + 2x3 + 4x4 = 0. Find a linear…

Q: Let T: R² P2 {where Pn denotes the vector space of polynomials with real coefficients that have…

A: The objective of this question is to prove that the given transformation T from R^2 to P2 is a…

Q: Let P, denote the vector space of polynomials in the variable a of degree n or less with real…

Q: let T be a linear operator on a finite- dimensional vector space V, and let f(t) be the…

Q: Let Pn denote the vector space of polynomials in the variable x of degree n or less with real…

Q: Let P, denote the vector space of polynomials in the variable æ of degree n or less with real…

Q: Let Pn denote the vector space of polynomials in the variable x of degree n or less with real…

Q: Let P3 be the vector space of polynomials of degree at most 3, with real coefficients. Consider the…

Question

Let P4 = set of polynomials with degree less than or equal to 4, and

T: P4 → P4

f → f′ (derived), ie T(f)=f′.

Judge the following statements as true or false

(a) The subset of P4 defined by N = {T ∈ P4 | T(p(x)) = 0} is a vector subspace of P4.

(b) T is not a linear transformation.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let P, denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let D: P3 → P₂ be the function that sends a polynomial to its derivative. That is, D(p(x)) = p' (x) for all polynomials p(x) E P3. Is D a linear transformation? Let p(x) = a3x³ + a₂x² + ₁x + ao and q(x) = b3x³ + b₂x² + b₁x + bo be any two polynomials in P3 and c E R. a. D(p(x) + q(x)) = D(p(x)) +D(q(x)) = + Does D(p(x) + q(x)) = D(p(x)) + D(q(x)) for all p(x), q(x) E P3? choose b. D(cp(x)) = c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all c ER and all p(x) E P3? choose c. Is D a linear transformation? choose (Enter a3 as a3, etc.) + +
Let Pn denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let D : P3 - P2 be the function that sends a polynomial to its derivative. That is, D(p(x)) = p' (x) for all polynomials p(x) = P3. Is D a linear transformation? Let p(x) = a³x³ + ²x² + a₁ + a₁ and q(x) = b3x³ + b₂x² + b₁x + b₁ be any two polynomials in P3 and c E R. a. D(p(x) + q(x)) = . (Enter a3 as a3, etc.) D(p(x)) + D(q(x)) = Does D(p(x) + q(x)) = D(p(x)) + D(q(x)) for all p(x), q(x) = P3? choose b. D(cp(x)) = + c(D(p(x))) = = Does D(cp(x)) = c(D(p(x))) for all CER and all p(x) = P3? choose ✪ c. Is D a linear transformation? choose ◆
Let T: P → P, be the linear transformation satisfying T (x² + 8) = 3x² + 3x + 1, T (3x) = 12x, and T (2x – 7) = 8(x+ 9). Determine T (ax + bx + c), where a, b, and c are arbitrary real numbers.
Let V be a vector space, and T :V →V a linear transformation such that T(5v1 + 3v2) = 401 – 402 and T(301 + 202) = 2v1 + 572. Then T(7) T(52) T(201 – 202) =
Let denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let D: 03 → be the function that sends a polynomial to its derivative. That is, D(p(x)) = p'(x) for all polynomials p(x) E 3. Is D a linear transformation? Let p(x) = a3x³ + a₂x² + a₁x + aº and q(x) = b3x³ + b₂x² + b₁x + bo be any two polynomials in 3 and c E R. a. D(p(x) + q(x)) = D(p(x)) + D(q(x)) = Does D(p(x) + q(x)) = D(p(x)) + D(q(x)) for all p(x), q(x) = ? choose b. D(cp(x)) = c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all c ER and all p(x) E 3? choose c. Is D a linear transformation? choose . (Enter a3 as a3, etc.)
Let Tv = Av represent the linear transformation T: R2 → R3 where 1 2 A = -2 4 -2 2]
Suppose that T: R2 --> R2 is a linear transformation such that T (i) = (1,2) and T (j) =(2,4_ . Show that T is not onto by finding one vector in the codomain that is not the image of any vector in the domain. Is T one-to-one?
Suppose T: R¹ → R™ is a linear transformation and {V₁, V2, V3}) is a set of vectors in R". (a) Complete the following definition: The set {V1, V2, V3} is called linearly independent if (b) (c) T is one-to-one if and only if Ker (T) = Show that if T is one-to-one and {V₁, V2, V3} is linearly independent, then the set {T(V₁), T(V₂), T(V3)} is linearly independent.
Let e1= (1,0) e2=(0,1), x1=(1,6) and x2=(4,−5) Let T: R2→R2 be a linear transformation that sends e1→x1 to and e2→x2. If T maps (−5,−8) to the vector y→, then y = ___