For each space below, determine the dimension of each space. Then indicate with or T or F if the space spans the overarching space.-4-41) Let S be the span of the vectorsThe dimension of this space is :This space would span all of R¹ :2) Let S be the span of the vectorsThe dimension of this space is :This space would span all of R¹ :3) Let S be the span of the vectors38306433-2The dimension of this space is :This space would span all of M22 (R):4) Let S be the span of the vectorsThe dimension of this space is :This space would span all of M22(IR):REtwó2017 30-8

*By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Answered: For each space below, determine the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 30E

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a) Determine if the vectors are linearly dependent or independent. b) Is it possible for the set (V1, v2,03, V4} to be considered as a base of R4 c) Consider the set H = Gen{V,02,03, vA) Is it a linear space? If so, how is its dimension found?
A set W is defined as consisting of all the planes in R^3 that are parallel to the plane x+2y-3z=1. If two elements of W are added to one another, is the result still in W? Why or why not? (PleaE give detailed explanation)
What should k be if the vectors x=(1,1,k) y=(1,3,1) z=(k,1,3) are in the same plane in the Euclidean space R3
can you solve the following problems? 1. Let B = {v1,v2,...,vk} be a set of vectors in the space R5. The set of vectors B spans R5 if for every element v ∈ R5 there exist numbersα1,···αk ∈Rsuch thatv =What is the minimal value of k for which this is possible?k = 2. Let B = {v1,v2,...,vk} be a set of vectors in the space R4.a) Complete the following definitionsDef. 1. The set of vectors B spans R4 if for every element u ∈ R5 there exist numbersα1,···αk∈Rsuch thatu =What is the minimal value of k for which this is possible?k =Does the following vectors span R4 -Why or Why not??-Explain.a1 = <3, cos 10, sin 11, 1> a2= <0, tan 13, sin 50, 2> a3= < √2, 0√23, −√7> 3. the matrix A= 1 0 1 1 2 0 0 1 1 1 0 0 0 1 1 d) Find a basis B1 of ColA consisting entirely of columns of A.(e) Find a second basis B2 of ColA consisting entirely of columns of A, or explain why such abasis does not exist.
State (with a brief explanation) whether the following statements are true or false. a) Let v1, v2, v3, be vectors in a space V. If v is a linear combination of v1 and v2, it is also a linear combination of v1, v2, v3. b) It takes at least three vectors to span R3. c) Every space has a unique set of vectors that spans it. d) Span {v1, v2} is the same space as Span {v1, 2v2}. e) Every set of three vectors in R2 is linearly dependent.
Find a condition on a, b, c so that (a, b, c) ∈ R^3, belongs to the space spanned by →u = (2, 1, 0), →v = (1, -1, 2), and →w = (0, 3, -4)
For each of the following vector spaces, give two differ- ent spanning sets: (a) R3 (b) M22 (c) P2
20 What is the size of the space stretched by the vectors {(1,0,2,0,1),(2,1,4,1,2),(1,1,2,1,1)}? a) 4 B) one NS) 2nd D) 3 TO) 0
Suppose {u1,u2,...,un} is a set of vectors that span V, and that {v1,v2,...,vk} is an independent set of vectors in V. Explain whyv1=x1u1+x2u2+...+xnunmust have a nontrivial solution. Explain why we may assume x1≠0. (Hint: x1 is the first unknown because u1 was the first vector in our spanning set.) Explain why this means u1 is in the span of {v1,u2,...,un} Explain why this means {v1,u2,...,un} also spans V.
Suppose we have a set of vectors v_1...v_n such that v_1 could be written as a linear combination of v_2...v_n. Prove that the Span {v_1...v_n}=Span {v_2...v_n}.
With the given operations, is R2 a vector space? Why or why not?

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For each space below, determine the dimension of each space. Then indicate with or T or F if the space spans the overarching space. 1) Let S be the span of the vectors The dimension of this space is : This space would span all of R4: bú b S20