Confused. Please help:) Let W be the set of all 1st degree polynomials (or less) such that p-p^2. Which statement is TRUE about W?OA. W is emptyOB. W is closed under scalar multiplicationOC. W is NOT closed under +O D. W doesn't contain the zero vector

Given W the set of all ist degree polynomials such that p=p2 Let p= 1 ⇒12= 1 Thus p=p2…

Answered: Let W be the set of all 1st degree…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 55RE

See similar textbooks

Similar questions

Find the quartic (fourth-degree) polynomial function f with real coefficients that has 1,2and2i, as zeros, and f(1)=10.
Let u1 = (1, 3, 2, 1), u2= (2, −2, −5, 4), u3 = (2, −1, 3, 6). If v = (2, 5, −4, 0), write v as a linear combination of u1, u2, u3. If it is not possible say so. Let V be the set of all fifth-degree polynomials with standard operations. Is it a vector space? Justify your answer. Let V = {(x, y) : x ≥ 0, y ≥ 0} with standared operations. Is it a vector space. Justify your answer. Let S = {(6, 2, 1),(−1, 3, 2)}. Determine, if S is linearly independent or dependent? Let S= {(1, 0, 0),(0, 4, 0),(0, 0, −6),(1, 5, −3)}. Determine, if S is linearly independent or dependent.
Show that the set of all real polynomials with a degree n < 3 associated with the addition of polynomials and the multiplication of polynomials by a scalar form a vector space.
From 1.21 and 1.22 linear algebra show all work
write in full sen
6. P2 denotes the set of all polynomials of degree ≤ 2, in a single variable x, with real number coefficients. P2 is a vector space under the usual operations of polynomial addition (combining like terms) and scalar multiplication. Determine whether each set of polynomials in P2 is linearly independent or linearly dependent. If the set is linearly dependent, find a dependence relation. If the set is linearly independent, demonstrate that any dependence relation has to be trivial. (a) {2x, x+3} (b) {x, 2x+5, 10} (c) {x² + 5x+1, x²-7x, x² +10, 2x² + 3x-4} 1ST (d) Make a linearly independent set of three polynomials in P2. Explain how you know.
Why do the set of all polynomials of degree n or less form a vector space, while the set of all polynomials of degree n or more do not?

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781337282291

Author:

Ron Larson

Publisher:

Cengage Learning

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra

Algebra

ISBN:

9781337282291

Author:

Ron Larson

Publisher:

Cengage Learning

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Let W be the set of all 1st degree polynomials (or less) such that p-p^2. Which statement is TRUE about W? OA. W is empty OB. W is closed under scalar multiplication OC. W is NOT closed under + O D. W doesn't contain the zero vector