Answered: Let W = {(a, b, c, d)| 5a – c = 0 } be…

Let W = {(a, b, c, d)| 5a – c = 0 } be a subspace of R. Then a basis for W is %3D O {(1,0,5,0),(0,1,0,0),(0,0,0,1)} O (1,0,5,0)} O {(5,1,0,0),(0,0,1,0),(0,0,0,1)} O {(1,0,5,0).(0,0,0,1)}

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 25CR

See similar textbooks

Related questions

Q: (c) Use the Gram-Schmidt orthogonalization process to find an orthogonal basis and an orthonormal…

A: We have to find orthogonal bases and orthonormal basis.

Q: Let R have the Euclidean inner product, and let W be the subspace spanned by the vectors uj = (1, 0,…

Q: Consider the subspaces of R5 U = span {⃗u1 = (1, 3, −2, 2, 3), ⃗u2 = (1, 4, −3, 4, 2), ⃗u3 = (2, 3,…

Q: Let {u1 (x) = -3, u2 (x) = – 12x, u3 (x) = -84²} be a basis for a subspace of P2. Use the Gram-…

Q: 11. Find a basis of the following subspace of R4. all vectors of the form (a, b, c, d) where a + b –…

A: The solution is given as

Q: Let V be a subset of R³ consisting of all solutions to the linear system x-y-5z=0. Show that V is a…

Q: Let W = {(0,x, y, z): x + 6y – 9z = 0 } be a subspace of R*. Then a basis for W is: {(0,6,1,0),…

Q: Let W = {(a, b, c, d)| 5a - b = 0} be a subspace of R*. Then a basis for W is O…

A: Just note that b=5a and then just separate out in good manner.

Q: 11. Find a basis of the following subspace of R4. W = all vectors of the form (a, b, c, d) where a +…

A: To find: Basis of W={(a,b,c,d) | a+b-c+d=0}.

Q: The set B=(v= (1,1,1),u=(0,0, - 3),w=(2,2,0)) IS: OA Linearly independent in R3. OBa subspaces of R.…

Q: Let W = {(a,b,c, d)| 5a – b = 0} be a subspace of R'. Then a basis for W is O {(1,5,0,0),(0,0,0,1)}…

Q: 2. Let H be the set of all vectors of the form (a – 3b, b – a, a, b) where a and b are arbitrary…

A: Let V be a vector space. H is said to be a subspace of V. If H is a subset of V. H is closed with…

Q: Let W be the subspace of R$ spanned by the vectors w,=(2, 2, -1, 0, 1), w2=(-1, -1, 2, -3, 1),…

Q: Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 1, O),…

Q: Let W = {(0,x,y, z): x- 6y + 9z = 0} be a subspace of R. Then a basis for W is: {(0,6,1,0),…

A: First option is correct

Q: What is the basis of the subspace below? W = {(x, y, z)€R³: x + y = 0} {(1,–1,0), (0,1,0), (0,0,1)}…

Q: Which of the following is a basis for the subspace {:) X y z x = y+z and x, y,z €RC M2x3(R) ? 0 x 0…

Q: Let W be the subspace of vectors in R3 that are orthogonal to w = (-1, 1, 1). Find a basis for W.…

Q: Consider the following subspaces of R': U = span[(1,3, -2,2), (1,4, –3,4), (2,3,-1,-2)] W =…

Q: 2. Let W be the subspace of R4 generated by the vectors (1, –2, 5, –3), (2,3, 1, –4) and (3,8, –3,…

Q: Let W = {(a,b, c, d)| a – 5 b = 0 } be a subspace of R*. Then a basis for W is O…

A: Given vector subspace of R^4 is

Q: Let W = {(a, b, c, d)| a - 5 b = 0} be a subspace of R*. Then a basis for W is %3D O…

Q: Let W = {(a, b, c, d) : a + 2b = c, d= 3a} be a subspace of R', then one of the following is a basis…

Q: Let W be the subspace of R' orthogonal to u1=(2, 1, -3 , 1) and u2=(0, 2 , -1 , 1), that is, W=S+,…

A: Here we use the gram Schmidt process to find orthogonal basis as follows

Q: Let V be the subspace of ℝ4 spanned by the columns of the matrix A=[1 2 3 −2 3 8 5 1 −3 −3 −4 −5 ]…

A: (a)Consider the given matrix, the columns of which spanned V:

Q: Let W = {(0, x, y, z): x + 6y- 9z = 0} be a subspace of R. Then a basis for W is: O (0,6,1,0),…

A: Basis for a subspace of a vector space

Q: Let W = {(a, b,c, d)[a - 5 b = 0} be a subspace of R. Then a basis for W O…

A: Given that W=a,b,c,d| a-5b=0 is a subspace of ℝ4.

Q: #6. Let W be the subspace of R³ spanned by the two vectors (1, – 1,1) and (3, – 2,0). Which one of…

Q: Let W = {(a, b,c, d)| 5a – b = 0} be a subspace of R*. Then a basis for W is O {(1,5,0,0),(0,0,0,1)}…

A: Basis of a vector space is a vector which has every element writen in a unique way a finite linear…

Q: Let W = {(a, b,c,d)| 5a - b = 0} bẻ a subspace of R'. Then a basis for W is %3D ((1,5,0,0)} O…

A: option b is correct answer . below is the explanation

Q: Let W = ((a,b,c, d)| a-5 b 0) be a subspace of R. Then a basis for W is O…

A: Basis for a subspace

Q: Let W = {(x,y, z): x – 6y + 8z = 0 } be a subspace of R³, Then a basis for W is: O (2,1,0),(-8,0,1)…

Q: Let W = {(a, b, c, d)| 5a – c = 0 } be a subspace of R. Then a basis for W is O…

A: We find basis of W subspace of R^4

Q: Find a basis for the given subspace of R°, and state its dimension for the plane 3 x- 2 y+ 5 z = 0.…

A: We have the vector space R3 , the subspace here is: W={(x,y,z) | 3x-2y+5z=0 ; x, y, z∈R}

Q: Let W {(a, b, c, d)| 5a- c 0} be a subspace of R. Then a basis for W is O ((1,0,5,0),(0,0,0,1)} O…

A: Find the basis for a subspace

Q: 2. Let W be the subspace of R5 spanned by the vectors (1,1,1,1,1),(1,0,1,0, 1), (0,1,1,1,0),…

A: For the solution of the problem follow the next steps.

Q: Which of the following sets form a basis for the W = {(a,b,c): b+3c=0} R³ of subspace ? {(1,0,0),(0,…

Q: Let W = {(x,y,z): x – 6y + 8z = 0 } be a subspace of R³. - Then a basis for W is: O…

Q: Let H be the set of all vectors of the form (a – 3b, b – a, a, b) where a and b are arbitrary…

Q: Let W be the subspace of R* with an orthonormal basis S = {w,,W2, W3}, where (0, 1, – 1, 0), w, =…

A: Given:- Let W be the subspace of ℝ4 and orthonormal basis S=W1,W2,W3…

Q: Let H={p € P3: p(0)=p(1)%3D0} be a subspace of P3. Show that 8 = {-2+2t, - is basis for H using…

A: Given: H={p∈ℙ3:p(0)=p(1)=0} is a subspace of ℙ3 B={-2t2+2t,t3-t} To show that B is a basis for H…

Q: Let W = {(a, b, c, d)| a – 5 b = 0 } be a subspace of R. Then a basis for W is %3D O {(1,5,0,0)} O…

A: Let W be subspace of R^4 then we find basis of W

Q: Find a basis for the given subspace of R°, and state its dimension for the plane 2 x - 4 y+ 5 z = 0.…

Q: Find a basis for orthonormal complement W- for a set W, a subspace in R* W = [2x, + x, + X + 2x, = 0…

Q: Let H be the set of all vectors of the form (a – 3b, b - a, a, b) where a and b are arbitrary…

Q: Let W = {(a, b,c, d)| 5a – b = 0 } be a subspace of R'. Then a basis for W is %3D…

A: The basis for W is given as follows

Q: Let H span {(-13, –1, -3),{-9,2, –2), (-1, –5, 0)}. A basis for the subspace H C R³ is { }. vector…

Q: Let W be the subspace of R4 orthogonal to u1=(2, 1, -2, 2) and u2=(0, 2, -2, 1), that is, W=S⊥,…

Q: Let W = {(0,x, y, z): x – 3y + 9z = 0 } be a subspace of R*. Then a basis for W is: {(0,3,1,0),…

A: A basis B for a vector space V is a linearly independent subset of V that generates V. And 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

noose The beST answer.
Let W = {(a, b, c, d)| 5a - c = 0 } be a subspace of R. Then a basis for W is
%3D
O {(1,0,5,0),(0,1,0,0),(0,0,0,1)}
O (1,0,5,0)}
O (5,1,0,0).(0,0,1,0),(0,0,0,1)}
O {(1,0,5,0),(0,0,0,1)}

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

Given

VIEW

solution

VIEW

Step by step

Solved in 2 steps

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 the bases for the four fundamental subspaces of the matrix. A=[010030101].
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.
Calculus Let B={1,x,ex,xex} be a basis for a subspace W of the space of continuous functions, and let Dx be the differential operator on W. Find the matrix for Dx relative to the basis B.
Proof Prove that if S1 and S2 are orthogonal subspaces of Rn, then their intersection consists of only the zero vector.
Calculus Repeat Exercise 45 for B={e2x,xe2x,x2e2x}. 45. Calculus Let B={1,x,ex,xex} be a basis for a subspace W of the space of continuous functions, and let Dx be the differential operator on W. Find the matrix for Dx relative to the basis B.
Calculus Use the matrix from Exercise 45 to evaluate Dx[4x3xex]. 45. Calculus Let B={1,x,ex,xex} be a basis for a subspace W of the space of continuous functions, and let Dx be the differential operator on W. Find the matrix for Dx relative to the basis B.
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
Spanning the Same Subspace In Exercises 61and 62, show that the sets S1and S2span the same subspace of R3. S1={(0,0,1),(0,1,1),(2,1,1)} S2={(1,1,1),(1,1,2),(2,1,1)}
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.
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.