-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 = 1 Из 5 u4 = -1 and ug = -1 16 -2 1 5 1 Note that u1, U2, Uz, U4 and ug are orthogonal. Uz+ Uz+ U4+ U5 CO

-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 = 1 Из 5 u4 = -1 and ug = -1 16 -2 1 5 1 Note that u1, U2, Uz, U4 and ug are orthogonal. Uz+ Uz+ U4+ U5 CO

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 59CR

See similar textbooks

Related questions

Q: Determine the dimensions of the following subspaces of R* a) All vectors of the form (a, b, c, d),…

A: We have to find the dimensions of vector

Q: 7 4 -7 find the closest point to v in the subspace W spanned by 2 and 4 -2 Given i -32

A: The given problem is to find the closest point to vector v in the subspace W spanned by given…

Q: Q-3: a) [10 marks] Find the dimension of the subspace a + 3c + b +c 2с— b 2а + 3b b) [10 marks] Find…

Q: O Linear subspace L is given by the equations 2r1 + r2 + 3r3 - 14 = 0 = 0 3r1 + 2r2 – 2r4 3r1 + 12 +…

A: Let AX=0 213-1320-2319-1x1x2x3x4=000R2→R2-32R1 , R3→R3-32R1…

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: -5 5. 10 8. Let A= 4 -7 -11, and define W = {C E M2x3 CA = 02x3}- %3D %3D -2 7. a. Prove that W is a…

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: The vector a can be projected onto the subspace spanned by uj and 02. This resulting projection of ā…

A: We are given that a→=-1-1011, v1→=1825, v2→=20-19-4 and vector a→ is projected onto the subspace…

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: 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: 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: 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: 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: 1 2 -5 11 -3 2 4 -5 15 2 Given that the matrix A = is row equivalent t 1 2 0 4 3 6 -5 19 -2 12 -5 11…

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: 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: -11 -3 1 2 Find the orthogonal projection of v = onto the subspace W spanned by 43 -5 -3 3 4 5 projw…

A: Given: v→=-11243-3 and W is a subspace spanned by -32-53, -3254, 12-35.

Q: 4 11 5 -7 -97 0 1 4 11 5 -7 -97 6. is row equivalent to B= 5 -2 -4 2 4 3 3 3. If A= -1 1 find bases…

A: Given the matrix is A=4115-7-9-2-4246-107105-3-7028 which is equivalent to…

Q: linear algebra problem

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: -5 -1 and v = 9 Let vi = Let W be the subspace spannd by the u's. Use the -9 3 Gram-Schmidt process…

Q: Which of the following are vector subspaces of of IR³? a) all vectors of the form (a, b, c), where b…

A: a) all vectors of the form (a,b,c), where b=a+cb) all vectors of the form (a,b,c), where b=a+c+1

Q: Determine if y is in the subspace of R4 spanned by the columns of A. -5 15 -6 -9 7 -7 -8 A = 6 13 y…

Q: S = {u1, u2, Uz3} and T = {v1, v2, V3} be two ordered bases for a subspace W in R". Suppose w1, w2,…

Q: 2 7 -6 find the closest point to v in the subspace W spanned by -4 9. Given v = -2 and 2 -9 -18

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

Q: 16 13 Given v = 59 find the coordinates for v in the subspace W spanned by -2 -2 -3 -1 -2 u1 = - u2…

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

Q: Determine if y is in the subspace of R spanned by the columns of A. 14 -5 -8 -7 A= 16 6-7 y= -5-7 3…

A: If y is subspace of R4 spanned by the columns of A

Q: -1 3 -3 1/2 Let u1 4 U2 = ,03 = 6. and 4 = -2 be vectors in R. Let B = {ũ1, 02} and C = {v3, v4}.…

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: Find the closest point to y in the subspace W spanned by v, and v2. 1 - 2 - 1 1 2 y = V1 = 1 %3D V2…

A: The closest point to y in W is the projection of y on W.

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: W, = (/:(4) = 3 +f(2)} W,= S: 2(3) =(1)} W, = (S:(5) = 0}. Then (a) W, alone is a subspace (b) W,…

Q: Find the closest point to y in the subspace W spanned by v, and v2. 3 1 - 1 - 4 - 1 y = 1 1 ,V2 - 1…

Q: (a) Find the matrix P describing the projection from R³ onto the subspace V = span{ 2 } 5. (b) Find…

A: The complete solutions are given below

Q: I For ū=(3,4,0,4) and =(-3,3,-5,6), calculate 7(u-40). II Determine if W = {" °: a, b, and c are…

A: You have asked many questions, As per the answering guidelines, We are supposed to solve first…

Q: 3 9. 28 Let vị = -3 ,U2 = -10 ,U3 = -29 and w = 10 5 15 45 1. Is w in {v1, v2, V3}? Type "yes" or…

A: Here 1,4 and 2,3 are same question. We know if determinate of vectors is not equal to zero.Then…

Q: 1 3 6. (4) (a) Find orthonormal vectors ĝ1, 2 in the subspace Span{a, b} spanned by ä = 7 of R5. 1…

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: (4) Linear subspace L is given by the equations 2r1 + 12 + 3r3 - 14 3r1 + 2r2 – 2r4 3ri + 12 + 9r3 -…

Q: 1. W is the set of all 2x2 matrices of the form 0 a where a and b are real numbers. Does W 3 b form…

A: Given, W is the set of all 2×2 matrices of the form 0a3b, where a and b are real numbers. To…

Q: 2. Find a basis for the subspace W = {[x y z]T : ax + by + cz = 0, a,b, c € R} of R". What is the…

Q: -1-日 5 Let S be the subspace of R° spanned by the vectors and 2 2 . Find the matrix P for the…

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems.

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 =
7
-10
find the coordinates for v in the subspace W spanned by
1
-7
-4
-1
2
3
-2
1
U2 =
1
Из
5
u4 =
-1
and ug =
-1
16
-2
1
5
1
Note that u1, U2, Uz, U4 and ug are orthogonal.
Uz+
Uz+
U4+
U5
CO

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

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 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 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.
Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
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.
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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.
Find the projection of the vector v=[102]T onto the subspace S=span{[011],[011]}.
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.
Proof Prove that if S1 and S2 are orthogonal subspaces of Rn, then their intersection consists of only the zero vector.
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.
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 rational numbers.