Answered: (a) Check the set of functions A = {x,… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 48RE

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Question

(a) Check the set of functions A = {x, 3x²-1, 5x3 3x} for orthogonality on [−1, 1].
-
(b) Determine if S is a subspace of R4. If it is, find a basis and the dimension.
X1
x2
-
S =
2x2 3x40 CR
X3
ᏆᎪ

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Find a basis for R2 that includes the vector (2,2).
Use matrix multiplication to find the orthogonal projection of (-8, 5, 7) on the xy -plane. Let T denote the linear operator mapping each vector into its orthogonal projection on the xy -plane. Then T(-8,5,7) = ( Ma )
Consider below presented polynomials v1, v2, v3, v4in P2. v1 = 2t2 + t + 2 v2 =t2 - 2t v3 =5t2 – 5t + 2 v4 =-t2 - 3t – 2 Determine whether the vector v = t2 + t + 2 belong to span {v1, v2, v3, v4}or not.
Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by the vectors (-3,7) and (9,3). (Use symbolic notation and fractions where needed. Give your answer in the form (*, *).) G(u, v) =
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.
Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate vector relative to the basis B is [X]B=(4, 5). (Write your answer in the form (a, b) where a and b are real numbers.)
Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.
Are the vectors = [−5_3 −1], v = [02-1] and w = [-25 21 -8] linearly independent? Choose If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation below true. Jū+ ☐ v+ ☐ w = ō.
Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}. Find the change of coordinate matrix Pc->B and find the B coordinate vector of -3-4t+4t2 as a column vector
Let S be the subspace of R¹ consisting of the solutions to the following system of equations: x1-2x2-2x3-3x4 -2x1+7x2+10x3-6x4 -2x1+5x2+7x3-2x4 = 0 = 0 = 0 Give a basis for S. Number of Vectors: 1 {[]}

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