Determine whether the set of all 3-tuples of the form (x, y, z), where z = x –subspace of R3.– 2y, form a

If W is a subset of a vector space V over a field F, then W is a subspace of V, only if it satisfies…

Answered: Determine whether the set of all…

Math

Advanced Math

Determine whether the set of all 3-tuples of the form (x, y, z), where z = x – 2y, form a subspace of R3.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 34EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,

See similar textbooks

Related questions

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: Show that W = {(x1, x2): x1 ≥ 0 and x2 ≥ 0}, with the standard operations, is not a subspace of R2.

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

Q: Consider the subspace V of R4 given by 1 3 1 V = span || -1 1 1

A: Solution:-

Q: let S be the collection of vectors [x] (2x1 matrix )in R2 that satisfy the given…

A: S forms a subspace of R2

Q: let S be the collection of vector [x] (3x1 matrix) in R3 that satisfy the given…

Q: If X is the subspace of `∞ consisting of all sequences of zeros and ones, what is the induced metric…

A: We have given that , X is the subspace of l∞ consisting of all sequences of zeros and ones. We need…

Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 -1 -1 projw (7) = %3|

Q: Let A = { | 2.x |x € R}. Is A a subspace of R³? З Let B x + y + z = 0}. Is B a subspace of R³?

Q: Find the orthogonal projection of 4 onto the subspace W of R* spanned by 1 1 -1 projw (7) =

Q: can a subspace of R^n have a dimension less than n.

A: Yes , it can be .

Q: Let vị 2,v2 8,and w Determine if w is in the subspace of R generated by v1 and v2.

Q: Prove that the set ? = {(a + b, a -b): a and b are real numbers} is a subspace of ℝ2 with the…

Q: Let W { (а, b, а + 2b + с, 2а — Зc), а, ь, с€ R} %3D - 1. Show that W is a subspace of R4. 2.…

Q: {{},} Let W be the subspace of R3 spanned by write j = |3 3 as the sum of a vector in W and a vector…

Q: Let-{ », :x, y, a, b e R and x - a = y – b}.Is W a subspace?

A: We will use the one step test for vector subspace to check if W is a subspace or not. We know that…

Q: Let S consists of all vectors of the form (x, 0, y, 0) in R* whe y are real numbers. Determine…

Q: let H= { a b 0 \ a ∈ R and b∈ R.} Show that H is a subspce of R3 by showing that it…

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: Verify that W is a subspace of V. In each case, assume that V has the standard operations.{(x, y, 4x…

Q: Let W = :a +5c = 0} be a subspace of M22. %3D Then dimension of W is equal to: None of the mentioned…

Q: Suppose that X = ER' :z + y + z = 0 and ² + y² = z² Determine (with justification) whether X is a…

A: Given X=xyz∈ℝ3:x+y+z=0 and x2+y2=z2

Q: If V is infinite-dimensional and S-is an infinite-dimensional subspace, must the dimension of V/S be…

Q: 2. Determine if the set S consisting of vectors of the form b where abc = 0 is a subspace of R³.…

A: No, S is not a subsapce of ℝ3. Explanation: Here, s1=110 and s2=001 belong to set S. Then,…

Q: Find the orthogonal projection of onto the subspace W of R' spanned by -1 -1 -1 1 1 projw (7)

Q: Let X = c, the space of all conver gent sequenes and M == (xn) such that , = 0 then M is not…

Q: Show that W = {(a, 0, b)la, b = R} is a subspace of R³.

A: As per guidelines we are supposed to solve the maximum first questions only .kindly post another…

Q: Find the dimension of the subspace of all vectors in R3 whose first and third entries are equal.

Q: Show that the set W={(x,y,1)|x and y are real} is not subspace of R3.

Q: Let W be the set of all vectors of the form Na subspace of R³ 0 2

A: Here given that vector [a 0 2] We know that condition of subspace w is zero vector belong…

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: determine the dimension of the subspace of R3 spanned by the given vectors.

Q: (a) Determine whether the set of all vectors of the form (a,b,c), where b= a+c, is a subspace of R³.…

A: Consider the subset S of ℝ3 defined as, S=(a,b,c)∈ℝ3 | b=a+c Take a1,a2,a3,b1,b2,b3…

Q: Let W = {(" ):a = 2c = b = –3d} be a subspace of M22. Then dimension of W is equal to: None of the…

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

Q: The set of all points in R3 satisfying x + y - z = 0 is a subspace. Note that the set of point…

A: It is known that any subspace of ℝ3 should contain an additivities identity element 0, 0, 0.

Q: Show that the set of all polynomials of degree at most 3 forms a subspace of Pn.

Q: Find the dimension of the subspace W of R4 spanned by S = {v1, v2, v3} = {(−1, 2, 5, 0), (3, 0, 1,…

A: Dimension of a subspace W is given by the number of linearly independent vectors in the basis of W,…

Q: determine the dimension of the subspace of R3 spanned by the given vectors.

A: Determine the dimension of the subspace of ℝ3 spanned by the given vectors.

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: Given vectors are y=466−1, u1=1101, u2=−120−1 and u3=−1011. We have to write the vector y as a sum…

Q: Determine whether the set W is a subspace of R3 with the standard operations. w = {(x1, 0, x3): X1…

Q: Determine: if W = the set of all vectors in R2 whose components are integers is a subspace.

Q: Let V = R and W = {x|x = (x1, x2, 1)}, Is W a subspace of V?

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

Q: Show that W={(x1,x2,x3,x4) : x4-x3=x2-x1} is a subspace of R^4 spanned by vectors…

Q: Show that points on the plane x-2y+4z=0 form a subspace of R3

Q: let W={(x,,x,,1):x,,x, are real numbers} is W a subspace of R

A: False

Question

Determine whether the set of all 3-tuples of the form (x, y, z), where z = x –
subspace of R3.
– 2y, form a

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

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Relations$

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 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 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 1-4, let S be the collection of vectors in [xy]in2 that satisfy the given property. In each case either prove that S forms a subspace of 2 or give a counterexample to show that it does not. xy0
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.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=3, W={[a0a]}
Find the projection of the vector v=[102]T onto the subspace S=span{[011],[011]}.
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?