Determine if the set V = {at? | a € R} is a subspace of the...

Question

Question

Determine if the set V = {at? | a € R} is a subspace of the vector space P2 = {ao +ajt + azt? | ao, a1, az ER}. You may assum

Answer 1

Answer #1

Page No. loly x=at² 2 y= bt? (15 v is subspace of Po Note OEX (0=o t² - otot tot² as OER) V&0 let ayev A, BEIR consider, xty

Answer 2

Similar Homework Help Questions

Determine if the given set is a subspace of P4. Justify your answer. All polynomials of...

Determine if the given set is a subspace of P4. Justify your answer. All polynomials of degree at most 4, with integers as coefficients. Complete each statement below. The zero vector of P4 in the set because zero an integer The set v closed under vector addition because the sum of two integers an integer The set closed under multiplication by scalars because the product of a scalar and an integer an integer Is the set a subspace of P4?...
Let be the set of third degree polynomials Is a subspace of ? Why or why not?...

Let be the set of third degree polynomials Is a subspace of ? Why or why not? Select all correct answer choices (there may be more than one). a. is not a subspace of because it is not closed under vector addition b. is a subspace of because it contains the zero vector of c. is not a subspace of because it is not closed under scalar multiplication d. is a subspace of because it contains only second degree polynomials e. is...
Let H be the set of third degree polynomials Let H be the set of third...

Let H be the set of third degree polynomials Let H be the set of third degree polynomials {ax + ax? + ax3 | DEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). a. H is not a subspace of P3 because it is not closed under scalar multiplication b.H is a subspace of P3 because it contains the zero vector of P3 c. H is not...

Let H be the set of third degree polynomials H = {ax + ax2 + ax...

Let H be the set of third degree polynomials H = {ax + ax2 + ax aEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). 0 a. H is a subspace of P3 because it contains only second degree polynomials 1b. H is a subspace of P3 because it can be written as the span of a subset of P3 OcH is not a subspace of P3...
Let H be the set of third degree polynomials H = {ax + ax? + ax?...

Let H be the set of third degree polynomials H = {ax + ax? + ax? | aEC} is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). a. H is a subspace of P3 because it contains the zero vector of P3 b.H is a subspace of P3 because it is closed under vector addition and scalar multiplication c. H is a subspace of P3 because it can...
Let H be the set of third degree polynomials H = {ax + ax? + ax3...

Let H be the set of third degree polynomials H = {ax + ax? + ax3 | DEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). a. A is a subspace of P3 because it contains the zero vector of P3 | b. H is not a subspace of P3 because it does not contain the zero vector of P3 c. H is not a subspace of...

Let H be the set of third degree polynomials H = {ax + ax? + ax?...

Let H be the set of third degree polynomials H = {ax + ax? + ax? | aEC} Is H a subspace of P3? Why or why not? Select all correct answer choices (there may be more than one). a. H is a subspace of P3 because it contains the zero vector of P3 b. H is a subspace of P3 because it is closed under vector addition and scalar multiplication Oc H is a subspace of P3 because it...
DETAILS LARLINALG8 4.R.023. Determine whether W is a subspace of the vector space V. (Select all...

DETAILS LARLINALG8 4.R.023. Determine whether W is a subspace of the vector space V. (Select all that apply.) W = {f: f(0) = -1}, V = C[-1, 1] W is a subspace of V. W is not a subspace of V because it is not closed under addition. W is not a subspace of V because it is not closed under scalar multiplication.
Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of...

Question 1: Vector Spaces and Subspaces (a) Show that (C(0, 1]), R, +,), the set of continuous functions from [0, 1 to R equipped with the usual function addition and scalar multiplication, is a vector space. (b) Let (V, K, +,-) be a vector space. Show that a non-empty subset W C V which is closed under and - necessarily contains the zero vector. (c) Is the set {(x,y)T: z,y E R, y a subspace of R2? Justify.

DETAILS LARLINALG8 4.R.084. ASK YOUR TEACHER Determine whether each statement is true or false. If a...

DETAILS LARLINALG8 4.R.084. ASK YOUR TEACHER Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. () The set w = {(0,x2,x): and X" are real numbers) is a subspace of R. False, this set is not closed under addition...