Answered: Let the set S = {(1, 1, 1), (2, 3, 3),…

Let the set S = {(1, 1, 1), (2, 3, 3), (0, 1, 2)} spans R3, write the vector (4,6, 7) as a linear combination of vectors S.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 72E: Proof When V is spanned by {v1,v2,...,vk} and one of these vector can be written as a linear...

See similar textbooks

Related questions

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

Q: Show whether R³ of the set B is a base and find the coordinate vector of the vector u = (- 1, -5,9).

Q: Determine whether the following vectors in R are linearly dependent or independent: (a) (1,2, –3,…

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: a) If possible, express w as a linear combination of vectors u and v. w = (1,0, –7), u = (1,3,4), v…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: S=1,2,3,4,1,0,1,2,1,4,5,6 Here use definition of linear dependent set Let V be a vector space over…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

Q: (a) Write the vector w = (1,1, 1) as a linear combination of vectors in the set S given by S =…

Q: Let v,, v,, and v, be vectors in R. What can you say about the linear dependence or independence of…

Q: a) If possible, express w as a linear combination of vectors u and v. w = (1,0, –7), u = (1,3,4),v =…

Q: t, v1 = (1, 2, −1), v2 = (2, −1, 3), v3 = (3, 2, 3). Determine whether the vectors v1, v2, v3 are…

Q: (a) Show that the three vectors vị = (0, 3, 1, – 1), v2 =(6,0, 5, 1), and v3= (4, – 7, 1, 3) form a…

A: Given the three vectors v1=0,3,1,-1v2=6,0,5,1v3=4,-7,1,3

Q: 2. Determine whether the set of the vectors {V1, V2, V3, V4} are linearly dependent or independent.…

Q: If a, B, y are linearly independent vectors of V(R), show that a + B, B + y, Y +a are also linearly…

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

A: There are two types of quantities that exist in nature, one is scalar quantity and the other one is…

Q: (a) Show that the vectors v1 = (1, 2, 3, 4). v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

Q: Suppose for vectors u, v and w that – 3u + 5v + 2w = 0. What does this say about the set {u, v, w}?…

Q: In each part, determine whether the given vectors span R3. (a) vị = (2, 2, 2), v2= (0, 0, 3), v3 =…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: (a) Determine whether W= (0, 5, 4) can be expressed as a linear combination of the vectors v1 =…

Q: 3 Let λ ER, and consider the vectors u, v, w E R³ defined by u = (3, 3, −6) v = (6, 7, -12) w = (3,…

Q: Show that the vectors u1=(1, 1, 1), u2=(1, 2, 3), u3 =(1, 5, 8) span R3

Q: (a) Show that the vectors v1 = (1, 2, 3, 4), v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

A: (a) The given vectors are: v1=(1,2,3,4), v2=(0,1,0,-1), v3=(1,3,3,3)

Q: ) Show that the three vectors vị = (1, 2, 3, 4), v2= (0, 1, 0, – 1), and v3 = (1, 3, 3, 3) form a…

Q: Let u = (-1,4, 3), v = (2, 1, –4), w = (4, 11, h – 1). Determine the value for h so that w is in the…

Q: Consider the vectors u=1,1,3 v= -2,0,2 w= 1,-1,1 Is the set {u, v, w} linearly independent or…

A: our objective is to check the linear independntness.

Q: r₁v₁ + 1₂v₂+...+rkvk = 0 a) v₁ = (3,-1,2), v₂ = (5,4,-6) and v3 = (8,3,-4) b) v₁ = (1, -2), v₂ =…

Q: Let v,, v2, and v3 be vectors in R. What can you say about the linear dependence or independence of…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: 1) Let, a, b & c are constants such that:…

Q: Determine if each of the following set of vectors are linearly dependent or linearly independent.…

A: Given query is to find vectors are linearly dependent or indipendent.

Q: Given that the set of vectors {v1, v2, v3}, where the vectors belong to R3 are linearly independent.…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: First we will express vector s1 a linear combination of other vectors s2 and s3soing so will give us…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: Solution: If k=1 then (0,0)=-47(3,4)+167(-1,1)+1(4,0)

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

Q: In each part, determine whether the vectors are linearly inde- pendent or are linearly dependent in…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: We solve this in step 2

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: Given : s = {(1,2,3,4), (1,0,1,2), (3,8,11,14)}

Q: Show that the set is linearly dependent by finding a nontrivial Ilinear combination of vectors in…

A: Given S = {(3,2), (-1,1), (2,0)}

Q: 4) For each set S of vectors and b below, determine if b e span(S) and if it is, then express b as a…

A: If a vector is expressible as a linear combination of vectors of a set S then we say that this…

Q: (a) Show that the vectors v1 = (0, 3, 1, – 1), v2 = (6, 0, 5, 1), and v3 = (4, – 7, 1, 3) form a…

A: We have to check linear dependent

Q: Find the value of k such that the given vectors are linearly dependent. (1,0,1), (0,1,3), (2,k, -1

Q: Express the given vector X as a linear combination of the given vectors A, B and find the…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

Q: Let u+ v = (3, –2) and u – v = (-4, –3). (a) Find u and v. (b) Draw the vectors u, v, – u, - v, u+v,…

Q: Let u, v, w be three linearly independent vectors in a vector space. Determine a value of k, k . so…

A: Given that: u, v, w are three linearly independent vectors in vector space and S={u-5v,v-8w,w-ku}

Q: Determine whether the set of vectors in P, is linearly independent or linearly dependent. {-x + x2,…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: let a1,2,3,4+b1,0,1,2+c2,6,8,10=0,0,0,0 a,2a,3a,4a+b,0,b,2a+2c,6c,8c,10c=0,0,0,0 simplify…

Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

Let the set S = {(1, 1, 1), (2, 3, 3), (0, 1, 2)} spans R³^, write the vector (4,6, 7) as
a linear combination of vectors S.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Cartesian Coordinates$

Learn more about

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

Similar questions

Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.
Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v12v2,2v23v3,3v3v1} linearly dependent or linearly independent? Explain.
Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of its length. b u has the direction opposite that of v and twice its length.
Determine whether the vectors u=6,10 and v=5,3 are orthogonal.
Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check your work against the answers in the back of the book. Write w=(7,2,4) as a linear combination of the vectors v1, v2 and v3 if possible. v1=(2,1,0), v2=(1,1,0), v3=(0,0,6)
Proof When V is spanned by {v1,v2,...,vk} and one of these vector can be written as a linear combination of the other k1 vectors, prove that the span of these k1 vector is also V.