-77Given v =67-10find the coordinates for v in the subspace W spanned by1-7-13-21U21Uz =5U4 =-1and u5116-211511Note that u1, U2, Uz, U4 and ug are orthogonal.Uz+ |Uz+U5

Answered: Image /qna-images/answer/a10229e5-b965-4ca8-8b58-f6a2982e2d47.jpg

-7 7 Given v = 7 -10 find the coordinates for v in the subspace W spanned by -7 -4 -1 2 3 -2 U1 1 Uz 1 Uz = 5 U4 = -1 and u5 1 -1 16 -2 1 1 1 1 Note that u1, U2, U3, U4 and ug are orthogonal. v = Uz+|| Uz+ U4+ U5

-7 7 Given v = 7 -10 find the coordinates for v in the subspace W spanned by -7 -4 -1 2 3 -2 U1 1 Uz 1 Uz = 5 U4 = -1 and u5 1 -1 16 -2 1 1 1 1 Note that u1, U2, U3, U4 and ug are orthogonal. v = Uz+|| Uz+ U4+ U5

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

See similar textbooks

Related questions

Q: The sets B={[1 2 2 1]T; [1 0 2 0]T; [2 0 4 -3]T} and B'={[0 2 0 1]T; [2 1 4 -1]T; [1 2 2n 4]T}…

Q: Given: a = [1 1 0 -1] b = [ 0 1 2 1] c = [ 1 0 1 -1] d = [ 1 1 -6 -3] e= [ -1 -5 1 0] Suppose, x =…

A: The basis is a set of linearly independent vectors that spans the given vector space. A basis is to…

Q: B 1 Find the dimension of the subspace V span{v1, v2, V3, v4} in R³ where vị = 2 1 V2 = , V3 = and…

A: We find dimension of the subspace V

Q: Which of the following is a subspace of R? O A. All vectors of the form (a, 0,0). O B. All vectors…

A: Subspace of a vector space: A subset V of ℝn is said to be a subspace of ℝn if 1. The zero vector…

Q: 1 Given v = -1 4 find the coordinates for v in the subspace W spanned by -7 -4 2 3 -2 u1 = 1 , u2 =…

A: The vectors u1, u2, u3, u4, u5 are orthogonal. Therefore, ui·uj=0, for i≠j. Consider the given…

Q: -5 63 Given v -42 98 find the coordinates for v in the subspace W spanned by 4 3 3 -15 U2 and uz 1…

Q: 4 -1 20 2. Let u1 U2 and y = 3 Из -10 3 -2 -4 Let W = span{u1,u2, U3} (i) Find the orthogonal…

A: Given: W=spanu1, u2, u3, where u1=1023, u2=320-1, u3=0-13-2 and y=420-10-4. To find: (i) Orthogonal…

Q: S = {u1, u2, U3} and T = in R". Suppose wi, w2, w3 E W such that {v1, V2, V3} be two ordered bases…

A: We are entitled to solve only one question at a time and up-to 3 subparts only. Please post other…

Q: 1. One of the following spaces is a subspace of R? the other two are not. Determine the one that is…

A: Answer

Q: 3 -6 -4 -3 4 Let y = V1 = 1 5 -1 Compute the distance d from y to the subspace of R4 spanned by v₁…

Q: -5 6 Given v = 1 -8 find the coordinates for v in the subspace W spanned by -7 -4 2 3 -2 1 5 and u4…

Q: 2s 4s + 5t Let W be the set of all vectors of the form Show that W is a subspace of R* by finding…

Q: 1 2 7 Let v, = and w = - 1 3 8 2 a. Is w in {v1, V2, V3}? How many vectors are in {v1, V2. V3}? b.…

Q: [1 3 5 0 9 0 0 0 1 8 1 3 50 9 Find the four subspace for the given matrices. A

Q: -5 Given v 9 -3 find the coordinates for v in the subspace W spanned by

Q: a + 3b + 4d C+ d 14) Let H = :a, b, c, d in R -3a - 9b + 4c - 8d -C - d Find the dimension of the…

A: image is attached with detailed explnation

Q: 2s 3s + 4t Let W be the set of all vectors of the form Show that W is a subspace of R“ by finding…

Q: Given v = find the coordinates for v in the subspace W spanned by -7 u1 = and uz -1 -28 Note that uj…

Q: 1 - 2 - 3 Let v1 = V2 - 4 and w = - 1 Determine if w is in the subspace of R° generated by V1 and…

A: Span of vectors

Q: 10 2 8 4 2 - Let M 1 9 -5 – 10 3 4 10 (a) Row Space M is a subspace of R² for what value of j? (b)…

Q: 11 12 53 Given v = 6 " 109 12 find the coordinates for v in the subspace W spanned by -1 4 U1 = -4…

Q: 6 6 Let u, = 3 , u2 = -6 , and u3 1. Note that u, and u, are orthogonal. It can be shown that uz is…

Q: 5s + 5t 4t Let W be the set of all vectors of the form Show that W is a subspace of R* by finding…

Q: -3 Given v = 9 D 10 find the coordinates for v in the subspace W spanned by 1 U1 = and uz = 6 -4 -1…

A: See the attachment

Q: 65 3 Given v = 79 6 367 12 find the coordinates for v in the subspace W spanned by -4 -6 -2 and u2…

A: Let v = a u1 + b u2

Q: -3 Let Pi = P2 = nį and -1 4 2 3 2 3 let Hj be the hyperplane in R' through p, with n2 5 normal nj,…

Q: 7 Given v = -1 1 find the coordinates for v in the subspace W spanned by -1 4. U1 -2 and uz = -2 -2…

Q: Which of the following are subspaces of R°, if it is not explain briefly why not: (a) The zero…

A: As per guidelines, we will solve first three subparts only. We have to check which of the below are…

Q: a 2. Is the set of vectors of the form b a subspace of R³? Show your proof. a+2b] 3. Show that the…

Q: 5. Let W₁ = equal to (a) 0 and W2 = (b) 1 0 be subspaces of R³. Then dim(W₁ W₂) is (c) 2 (d) 3 V

Q: -(80) (b) 2. The subspace (a) x+y+z= By in R³ is a plane whose equation is x-2=0 (c) y x-2y+z=0 (d)…

A: Here i am using linear combination and then we saw the relation between the coordinates.

Q: -7 7 Given v = 7 -10 find the coordinates for v in the subspace W spanned by 1 -7 -4 -1 2 3 -2 1 U2…

Q: -4 - 1 - 2 and v, = - 1 1 Find the distance from y to the subspace W of R spanned by v, and v,,…

A: Given: y=3-1113,v1=1-2-12v2=-4103 and Closest point to y in W is y^=-1-5-39

Q: 3 - How many of the following statements are true? y + z +t = 2 The system x + 2y + z -t = -1 has no…

Q: 3 Let v, = V3= and w = .Is w in the subspace spanned by {v,, v2, Va}? Why? -1 3 Choose the correct…

Q: -5 -2 -4 Given v = find the closest point to v in the subspace W spanned by -2 and 7 70

A: Let consider v=−19−2−3, u1=−5−26−1, u2=−4−4770

Q: (b) Let A and B be 30 × 29 matrices. Show that there exists a vector c E R30 such that both the…

A: Question: Let A and B be 30x29 matrices. Show that there exists a vector c∈ℝ30 such that the system…

Q: ue 1. If the set of vectors U is linearly independent in a subspace S then vectors can be added to U…

Q: -8 Given v = -7 find the coordinates for v in the subspace W spanned by -1 4 -3 u1 3 , U2 and U3 -17…

Q: O b. The set of matrices of the form q b a,b ER is not a subspace of M2×2 1 c O c. If A is a 2×3…

Q: 43 12 19 12 Given v = 65 12 find the coordinates for v in the subspace W spanned by -1 4 Uj = and u2…

Q: - 5t Let H be the set of all vectors of the form 8t Find a vector v in R3 such that H = Span{v). Why…

A: Yes it is a vector space of R3 of dimension one because of option A

Q: 11 12 - 53 6 Given v = " 109 12 find the coordinates for v in the subspace W spanned by -1 4 U1 = -4…

A: We will write v as linear combination of u1 and u2 and then find values of

Q: 1 -2 -3 Let v, ,V2 - 7 and w -3 Determine if w is in the subspace of R generated by v, and v2. -6 11…

A: To determine If W is in tg subspace of R^3 generated by v1 and v2.

Q: 6 a. Show whether or not H= {(x,y, z)| 2x – y + 3z = 0} is a subspace of R3 p. Solve the following…

Q: Which of the following statements are/is TRUE? 6 1 (1) 5 3 is in the subspace of 2 x 2 matrices…

Q: 5s 5s + 5t Let W be the set of all vectors of the form Show that W is a subspace of R* by finding…

Q: -3 Set W to be the subspace of IR spanned by the vectors 2 -3 , and -3 Find a basis for W…

Q: 10 Let u, = - 8 , and uz 1 Note that u, and uz are orthogonal. It can be shown that u3 is not in the…

Q: The set W = 3x- y = z -5w = 0 is a subspace of R". What is the %3D %3D dimension of W Select one: а.…

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

-7
7
Given v =
6
7
-10
find the coordinates for v in the subspace W spanned by
1
-7
-1
3
-2
1
U2
1
Uz =
5
U4 =
-1
and u5
1
16
-2
1
1
5
1
1
Note that u1, U2, Uz, U4 and ug are orthogonal.
Uz+ |
Uz+
U5

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Given

VIEW

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 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

Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.
Proof Prove that if S1 and S2 are orthogonal subspaces of Rn, then their intersection consists of only the zero vector.
Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?
Subsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R3 whose components are nonnegative.
Subsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R2 whose second component is the square of the first.
Subsets That are Not Subspaces In Exercises 7-20, W is not a subspace of V. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R2 whose components are integers.
Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.
Subsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all matrices in Mn,n with determinants equal to 1.