Answered: {p(x) | p(-3)p(3) = 0} E. {p(=) | p(2)… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 11E

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Question

Solve for D, E, F, G, H

Select all subsets that are vector subspaces of P2(R)
{p{z) | p(-3) = P(3)}
А.
в. { ал? + ba + с За - 2с %3D b, а, b, с €1
eR}
c. {x2 + bx + c b, c eR
OD. {p(x) | P(-3)p(3) =0}
OF {p(=) | r(2) = 1}
O G. P2(R)
{p(=) | r(2) = o}
Н.
%3D
ui

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Determine if the vectors < -2,-1,1>, <3,-4,-2> and <5,-10-8> are linearly independent.
Select all subsets that are vector subspaces of P2(R) {p{z) | p(-3) = P(3)} А. в. { ал? + ba + с За - 2с %3D b, а, b, с €1 eR} c. {x2 + bx + c b, c eR OD. {p(x) | P(-3)p(3) =0} OF {p(=) | r(2) = 1} O G. P2(R) {p(=) | r(2) = o} Н. %3D ui
Let f([])= -6 u + 6 v be a real-valued function and let - [35] and find that f(z) - = 수 수 수 [23] be vectors. We (no arithmetic permitted in this answer) and f(3) = (no arithmetic permitted in this answer). Ifz--22+5y, then f(3) = (arithmetic is permitted in this answer)
Let V₁, V2, V3 be the vectors in R³ defined by 18 ---D V₁ = -6 V2 = -14 V3 = 20 (a) is (V1, V2, Vs} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V₂, and V3 0 (c) Type the dimension of span {V1, V2, V3}: Note: You can earn partial credit on this problem. -25 -18] 0=v₁+√₂+vs (b) Is (v1, vs} linearly Independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁ and V3. 0=v₁+v₁ V3
Suppose y1 ( x), y2 ( x), y3 ( x) are three different functions of x. The vector space they span could have dimension 1, 2, or 3. Give an example of y1, y2, y3 to show each possibility.
{ (1,2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii) Determine whether the vector (1,2, 6) is a linear combination of the vectors (1, 2, – 1), (3, 1, 1), and (-4, 0, 6). (Include all the steps in your reasoning.).
Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use s,, Sa, and s,, respectively, for the vectors in the set.) S = {(5, 2), (-1, 1), (4, 0)} 4 (0, 0) = | S1-두s2 + 두3 Express the vector s, in the set as a linear combination of the vectors s, and s,. S, =
(2) Determine if the vectors are linear independent or linear dependent. Justify your answer. (a) (4)(7): 1 -2 -2 (b) ()O(E) :) 4 -8 -6 (c) (E) 1 101 10001 2 102 10002 Vi = V2 >..*, V101 100 200 10100
Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is linearly independent. If yes, show work, if no state a linear combination among the vectors of the list that adds up to a vector in the list. I am having trouble grasping the concept so if anyone can explain this problem I'd appreciate it.
8. (a) Show that the vectors v1 = (1, 2, 3, 4), v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a linearly dependent set in R*. (b) Express each vector as a linear combination of the other two.

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