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 O {(5,1,0,0),(0,0,1,0),(0,0,0,1)} O {(1,0,5,0)} O ((1,0,5,0).(0,1,0,0),(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

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 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 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: Which of the following is a basis for the subspace {:)- x y z W = x = y + z and x, y,z E R}C M2x3(R)…

A: We have to satisfy the given condition in the matrix i.e. x = y+z

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: {{::] a Let W = : a, b, c, d in R is a subspace of the vector space M23. Find a basis for W. c d 0…

A: Given that W=a0bcd0:a,b,c,d∈R is a subspace of the vector space M23. We have to find the basis for W…

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: 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: a) In the vector space R3, let a = (1,2,1), ß = (3,1,5),y = (3,–4,7). Show that the subspace spanned…

A: We can solve this by finding the reduced row echelon form. We also know that elementary row…

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 be the subspace of R4 spanned by {u₁ = (1, 1, 1, 1), u2 = (2, 4, 1, 5), u3 (2, 0, 4,0)). Using…

A: The solution is given as

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: 10. Let W be the subspace of the real vector space V =R* spanned by a = (1,–1,2), 3 = (2, 3. –6), 7…

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 R5 spanned by the following vectors: u1=(1,2,1,3,2), u2=(1,3,3,5,3),…

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 = {(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 H span {(-11,0, –5), (–3,0, –1), (–2,0, –1)}. A basis for the subspace H C R³ is { vector

Q: Let w = ( { (x.y,z) ER3: x+y-z 0) be a subspace. A basis of w+ is [A].

A: Solution

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: Find a basis for the subspace of R* consisting of all vectors of the form (a, b, c, d) where c = a +…

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

A: Let W=a,b,c,d / 5a-c=0 be a subspace of R4.

Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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 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: Find a basis for the subspace of R* consisting of all vectors of the form (a, b, c, d) where c = a +…

A: To Find: Basis for the subspace of R2 of the form (a,b,c,d) such that c=a+7b and d=a-6b

Q: Let W be the subspace of R3 spanned by the following five vectors: u1=(0, 1, 0), u2=(1, 2, 0),…

Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A: We will find out the required solution.

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: 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 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 V be the vector space of 2 × 2 matrices over the real field R. Find a basis and 5 dimension of…

A: Given A=12-13B=251-1C=51211D=34-25

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

Let W = {(a, b, c, d)| 5a – c = 0 } be a subspace of R. Then a basis for W is
O {(5,1,0,0).(0,0,1,0),(0,0,0,1)}
O {(1,0,5,0)}
O (1,0,5,0).(0,1,0,0).(0,0,0,1)}
O (1,0,5,0).(0,0,0.1)}
Letk be a real numberand A=
Then determinant of A is

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 by step

Solved in 2 steps with 1 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 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.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn, W is the set of diagonal nn matrices
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?
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.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[a0a]}
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn,WAinMnn:detA=1
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 37. V = P, W is the set of all polynomials of degree 3
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba+b+1]}
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[aba]}