14. Let W be the subspace of R3 spanned by the vectors v=(1,0,7), v2=(6,1,7), andV3-(14,-1,13). Find bases for W and W.

Answered: Image /qna-images/answer/b2a68a03-a509-4343-9414-7bfc907467b4.jpg

Answered: . Let W be the subspace of R3 spanned…

. Let W be the subspace of R3 spanned by the vectors vj=(1,0,7), v2=(6,1,7), and V3=(14,-1,13). Find bases for W and W'.

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: Let W be the subspace of IRª spanned by the vectors 4 2 and -1 Find the matrix A of the orthogonal…

A: Consider the given information: Let W be the subspace of ℝ4 spanned by vectors :1-11-1,4-2-1-7 To…

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Using the orthogonal projection of vector Y to get the component of y along the vector space W.

Q: Show that V is a subspace of R³: V is the set of all (x, y, z) such that z = 2x + 3y

Q: Show that the set W : {(x, y, 5x-4y)| x and y are real numbers} is a subspace of R³.

A: We are give, W=x,y,5x-4y| x and y are real numbers To show: W is a subspace of R3 This can be done…

Q: Find the dimension of the subspace H of IR2 spanned by the vectors and

Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: Let X = 1 ,and let V = {A E M2(R) | AX = XA}, a subspace of M2(R). 0. Find a basis for V, and write…

Q: 4.) Determine the dimension of thr subspace of M21 consisting of vectors of the form [a – 2b] a + b…

Q: Find the closest point to y in the subspace W spanned by v, and v2. 13 1 5 - 1 y = 1 1 , V2 = 1 - 1…

A: Given y=13-112,v1=11-1-2,v2=5103. The orthogonal projection of y onto span of v1, v2 is…

Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw (v) |||| 6 V H 14 2 and…

Q: (c) Find a subspace U such that R³ = W₁ OU.

A: C. Hint: Use the result of part (b) in the part (c) and obtain the required result.

Q: - (-, s) Find a basis for the subspace W C R', consisting of all the vectors orthogonal to the…

Q: Determine: If W = the set of all vectors in R2 whose second component is the square of the first. is…

Q: a. . Is the set of vectors of the form a subspace of R³? Show your proof. La+2b

Q: Find the closest point to y in the subspace W spanned by u, and uz. 17 1 2 %3D u1 = 0 |, u2 = - 1 2…

A: To find The closest point to y in the subspace w spanned by u1 and u2

Q: Find the orthogonal complement S⊥ of the subspace S of R3 spanned by the two column vectors of the…

Q: The vector x is in a subspace H with a basis B= {b, ,b2}. Find the B-coordinate vector of x. x= [x]B

Q: Find an orthogonal basis for the subspace {(x, y, z) E R³ | x + 4y – 2z = 0} -

Q: Consider the sets of vectors of the following form. Prove that they are subspaces of R3. 1. (a,…

A: Solve the following

Q: Find the subspace spanned by the three vectors [2 3 1]T, [2 1-5]T, and [2 4 4]T Feuth

A: We will check the vectors that it is linearly dependent or linearly independent. If the vectors…

Q: Show that S = {(x, Y, z)|4x – y + 5z = 0, x, y, z E R} is a subspace of R³.

Q: Let S be the subspace of Rn spanned by the vectors x1, x2, . . . , xk. Show that y ∈ S⊥ if and only…

Q: Find the orthogonal projection of the vector v onto the subspace S. v = |2 S =

A: projS(V) = (u1.v/u1.u1)u1 + (u2.v/u2.u2)u2

Q: R? Which vector stretches the x + y = 0 subspace of ? Why is that? a. (2,1) b. (0,0) c.(1, -1)…

Q: For a certain subspace W, the orthogonal projection of the vector y = 3 onto W is ŷ 2. Use this…

Q: a Is the set of vectors of the form a subspace of R³? Show your proof. La+2b

Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: Find all values of h such that vector y will be in the subspace of R spanned by vectors 3. V1, V2,…

A: we will first find the equivalent matrix and then reduce it to row echelon form

Q: a. Is the set of vectors of the form a subspace of R3? Show your proof. La+2b|

A: Since you have asked multiple questions, we will solve the First Question for you. If youwant any…

Q: Let u, = 2 |, u2 and uz = 0 Note that u, and uz are orthogonal but that uz is not orthogonal to u,…

A: The orthogonal vector is given as follows :

Q: Find a basis and dimension of the subspace described as follows:{(x, y, z, w) |2x + 5y – z=0} (0-0)…

Q: Determine whether U = {(1, s, t)ls,t e R} is a subspace of R.

A: FOR ANY SUBSET U TO BE A SUBSPACE OF ANY VECTOR SPACE V IT IS NECESSARY THAT U HAS ZERO VECTOR IN…

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

Q: Find the dimension of the subspace of all vectors in R'whose second and third entries are equal. O…

A: Dimension of subspace is 6. Since dimension of R^7 is 7 and the given subspace has second and third…

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

Q: 9. Find the vector closest to y from the subspace of Rª spanned by Vị and v2. 3 1 Vị = 1 , y = V2 =…

A: To find The vector closest to you from the subspace of R^4 spanned by v1 and v2.

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

Q: Find the subspace generated by the vectors A= (2,1,-5), B= (4,3,7) %3D %3D So in space R³

Q: 4) Find all values of h such that Y will be in the subspace of 3. R spanned by VI) V2, V3 if V I V2…

Q: 9

Q: ) Do there exist subspaces S,T, and U of R³ such that S 1 T, SI U, and TiU? if so, provide an…

A: I have considered te subspace generated by orthogonal basis vector.

Q: Let W be the set of all vectors of the form b. 3c - 2 b C where b and ceR. Find vectors u and v such…

A: Spanning set

Q: Let U and W be subspaces of R³ for which dimU=1, dimW=2, and UgW. Show that R=UOW.

A: I have shown all the conditions of direct sum of two subspaces

Q: Let W be the subspace of IR spanned by the vectors and -6 7 Find the matrix A of the orthogonal…

Q: Find the distance from the point x = (1, 5, –4) of R³ to the subspace W consisting of all vectors of…

A: First we will find out the orthogonal basis for the subspace W. Then we calculate the orthogonal…

Q: Determine: if W = the set of all vectors in R^2 whose second component is the square of the first.…

Q: Let W be the subspace of R spanned by the vectors 3 and -6 12 Find the matrix A of the orthogonal…

Q: Q2. Check if the following points lies on the subspace U spanned by the vectors = [2 -1 2]', x2 = [0…

Q: Find the closest point to y in the subspace W spanned by vị and vz 2 1 y =| 1 |,v1 =| 0 [0] 2 lo] 2…

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

14. Let W be the subspace of R3 spanned by the vectors v=(1,0,7), v2=(6,1,7), and
V3-(14,-1,13). Find bases for W and W.

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

Trending now

This is a popular solution!

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, algebra and related others by exploring similar questions and additional content below.

Similar questions

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.
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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.
Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from R3 into R3 such that the set {T(v1),T(v2),T(v3)} is linearly dependent.
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 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?
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.
Find the projection of the vector v=[102]T onto the subspace S=span{[011],[011]}.