### Linear Algebra Concept CheckThe set $ S = \{v1, v2, \ldots, vn\} $ is a spanning set for the vector space $ V $. This statement implies that any vector $ u $ in $ V $ can be written as a linear combination of the vectors in $ S $.#### Question:Is it true that any vector $ u $ in $ V $ can be written in one and only one way as a linear combination of the vectors in $ S $?##### Select one:- ○ True- ○ False

Answered: Image /qna-images/answer/c256d755-5622-4406-bfe1-3af7e64b5821.jpg

Answered: The set S={v1, v2, ..., vn} is a…

The set S={v1, v2, ..., vn} is a spanning set for the vector space V, then any vector u in V can be written in one and only one way as a linear combination of vector of S. Select one: O True O False

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: solve all 132 q5

A: Step 1: Step 2: Step 3:Step 4:

Q: Let W be the set of all vectors of the form shown on the right, where a, b, and c represent…

A: See the detailed solution below.

Q: If set S={v1, v2, . . ., vn} is a spanning set of a vector space V, then any vector u in V can be…

A: Remark: We know that, if S is a spanning set for a vector space V , then every vector v in V must be…

Q: Suppose a₁, A2, A3, a4, and a5 are vectors in R3³, A = (a₁ | ª₂ | a3 | 24 | 25), and 1 0 0 -5 0 1 0…

Q: Let S = {u1, u2,..., uk } be a set of vectors in a vec- tor space and let T = {v1, v2,..., vm},…

A: Let V be the vector space let S=u1,u2,......uk be a set of vectors in V let T=v1,v2......vm be the…

Q: Find an explicit description of Nul A by listing vectors that span the null space. [ A = 1 -4 -5 0 0…

Q: 1 The vector is in the span of if and only if the system . ........ 3

A: A detailed solution is given below.

Q: Let u be a vector that is not a linear combination of {u₁, U₂, 1 U3,}- Select the best statement. A.…

A: Given is a vector that is not a linear combination of .To select the best statement out of the…

Q: Consider the vectors u1 = (1, 2, 1), u2 = (0, 3, 2) and u3 = (−2, 1, 1). Determine whether the set S…

A: The objective of this question is to determine whether the set of vectors S = {u1, u2, u3} spans the…

Q: Consider the following statement: If V1, V2, V3, V4 are vectors in IR such that no vector v; is a…

Q: Find an explicit description of Nul A by listing vectors that span the null space. A= 138 0 0 1 4 -5…

Q: Let B = {v1,v2,...,vk} be a set of vectors in the space R5. Which is the maximal number k for which…

A: Given B = v1, v2, ..., vk is a set of vectors in the space ℝ5.

Q: Let S = {[x y z] | 3x + 2y + z = 0} . Write the set S as the span of a set of two vectors in R 3

A: Let (x,y,z)∈Sthen 3x+2y+z=0 z=-3x-2yTherefore,…

Q: If both S1 and S2 are spanning sets for the vector space V, then S1 and S2 must have the same number…

Q: Find a, such that the set w-(1+2r-x?,a+x+x,5-5x+7x) is linearly dependent in the vector space R Ob.…

Q: 2. Determine if the following vectors constitute a linearly independent set.

Q: 6. Find L{f(t)} for the following periodic functions. S t, b. f(t) = 1 2n – t, 1<t < 27 0 <t< T f(t)…

Q: Do the following sets of vectors span R°? 3 12 No 1. -3 -12 3 11 100 2 -15] Yes 2. -23 4 -10 -2 Yes…

Q: 2. Each set below is a subset of R2. For each set, do the following: • Sketch a picture of the set.…

Q: 17. Determine whether each statement is true or false, and provide a justifica- tion or a…

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

Q: Suppose that {u, v} is a linearly independent set. Show that the set {u – v, u + v} is also linearly…

Q: 10. If 3(a, 3, 2)-2(3, b, b) = (-3, 1, -2), determine a and b. Describe the set spanned by the…

Q: Suppose that v = (v1, v2, ..., vn) and ū = (u₁, U2, ..., Un) are a pair of n-dimensional vectors.…

A: We have to define formally the predicate AlmostTheSame(v→,u→) for n dimensional vectors v→ and u→.

Q: Consider the vectors u1 = (1, 2, 1), u2 = (0, 3, 2) and u3 = (−2, 1, 1). Determine whether the set S…

A: The objective of this question is to determine whether the set of vectors S = {u1, u2, u3} spans the…

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

### Linear Algebra Concept Check

The set $ S = \{v1, v2, \ldots, vn\} $ is a spanning set for the vector space $ V $. This statement implies that any vector $ u $ in $ V $ can be written as a linear combination of the vectors in $ S $.

#### Question:
Is it true that any vector $ u $ in $ V $ can be written in one and only one way as a linear combination of the vectors in $ S $?

##### Select one:
- ○ True
- ○ False

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector Space$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Let W be the set of all vectors of the form shown on the right, where a, b, and c represent arbitrary real numbers. Find a set S of vectors that spans W or give an example or an explanation to show that W is not a vector space. 4a + 2b 5b + 2c 8c + 8a 7b Select the correct choice and fill in the answer box as needed to complete your choice. O A. A spanning set is S={} (Use a comma to separate answers as needed.) O B. There is no spanning set of W because W does not contain the zero vector. O C. There is no spanning set of W because W is not closed under vector addition. O D. There is no spanning set of W because W is not closed under scalar multiplication.
Compute the norm of the vector 7 = |||
Suppose {v1, v2, ..., vp} is an orthogoal set of vectors. Show that {c1v1, c2v2, ..., cpvp} will also be an orthogonal set, for any choice of scalars c1, c2, ..., cp.
Suppose X = {-3,-2,-1, 0, 1, 2, 3}. Let fuzzy subsets A and B of X be defined by their membership vectors A = [0.0, 0.3, 0.8, 1.0, 0.8, 0.3, 0.0] and B = [1.0, 0.9, 0.7, 0.5, 0.2, 0.0, 0.0] Determine the membership vectors (write the results as list of numbers rounded to 2 decimal places) Operation Model ANB minimum ANB product ANB drastic product AUB maximum AUB probabilistic sum AUB drastic sum standard
Let 4 be a linear combination of {u₁, 1₂, 13). Select the best statement. A. span{u₁, U₂, U3} = span{u₁, U2₂, U3, 14} when u4 is a scalar multiple of one of {U₁, U₂, U3}. B. span{u₁, U₂, U3} = span{U₁, U₂, U3, U4}. c. We only know that span{u₁, U₂, U3} span{u₁, U₂, U3, U4} . D. There is no obvious relationship between span{u₁, U₂, U3} and span{u₁, U₂, U3, U4} . E. none of the above
6. Let 7₁, 7₂, .... that {V₁, V₂, . . . . . ., Ủn, } is linearly dependent. Un be vectors in a vector space V and let 7 be any vector in the span of S = 9 Ủi, U2,... 2 Un}. Prove
S is a linearly independent set,then for any x element of , x is not the linear combination of other vectors in S. Is this true or false?
is the ffollowing set of vectors in P2 is liner independen? Prove the answer
Show that ||v||≤||v||₁||v|| about 1¹, 1², and 1 vector norms.
Suppose v1, v2, v3, 04, Ū5 and ve are vectors in R6 satisfying the following linear relation: 201 + 302 – Ủ4 + 205 - Which of the following must be true? (Select all that apply) span(v1, v2, v3, 4, 06) = span(71, v3, 74, 05, V6) span(v1, v2, v3, 74, 05) = span(v1, v2, v4, V5, 76) span(v1, v2, v3, v4, v6) = span(v1, 02, v3, v4, Ü5 , v6) span(v1, v2, V3, v6)= span(73, v4, V5 , V6) O span(v1, v2, v3, V4, 05) = span(72, 03, v4, 05, V6 )
Plz solve both