please answer this and show why they (a,b,c,d,e) are a subspace or not subspace 2. Determine which of the following is a subspace of R".(a) {(x1,x2,..x,) | x1=0}(b) {(x1, X2,.. , x,) | x1 2 0}(c) {(x,X2...X)1 x 2x}(d) {(x,X2..X) 1 =1-2x2}(e) {(x, X2...x) | x = X2 == X,}|3|

Answered: Image /qna-images/answer/aa38bba6-c238-433d-809f-0177682b405d.jpg

Answered: 2. Determine which of the following is…

2. Determine which of the following is a subspace of R". (a) {(x1,x2,...X) 1 x = 0} (b) {(x1, X2,...,x) I x 20} (c) {(x,X2.X)1x=2x2} (d) {(x,X2..x)1 x =1-2x} (e) {(*, X2.x,) I X=x,} %3D ....

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 38EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=F,W=finF:f(x)=f(x)

See similar textbooks

Related questions

Q: Question 3: A game of zumpie consists of 3 teams; 2 teams lose and 1 team wins. Fifty-one teams…

Q: an a) Converges n2 b) lim an =0 > cans converges dd) > cos (an) Converges n=1 e) Cos can) diverges

Q: Let X be a discrete random variable with , density function. = {1,2, 3, ..} and f(x) = as a (a)…

Q: Find the equation of the line that passes through the point (7, 3,4) and is perpendicular to the…

A: The given problem is to find the equation of line that passes through the point (7,3,4) and is…

Q: A Moving to another question will save this response. Question 7 For the given matrix A, find a…

Q: . Let G be a group of order 425. Prove that if H is a normal ubgroup of order 17 in G then H <Z(G).

Q: 41-45. In an employee selection of a company, 5 males and 4 females pass the test as the candidate.…

A: Since you have asked multiple question( second and third question) we will solve the second question…

Q: 1. What is a satisfiable formula of first-order logic? Any examples?

Q: prove that i } X is a Coun table set and P: X>Y is asurjecbive then Y is Countable

A: Note: X denotes cardinality of X, that is number of elements in the set X. If X is countable means…

Q: -3 1 -3 4 -1 4 If A = -3 -3 -2 and B = -4 -2 -2 -1 -1 -4 -1 -3 -2 3B = an

Q: If A is an n x n matrix and b + 0 in R", then consider the set of solutions to Ax = b. Select true…

Q: 3. Let f(x) = 1+x + x² + x³ + x“ + x5. (a) definition of Taylor polynomials. Find T3(x), the Taylor…

Q: Question (2) 으 (2-3)" P(군)= Let then : %3D a Determine Zo=? and ana? b) Determine the Covergance…

Q: Solve y/" – y" + y – y = e=' sin t.

Q: (a) if f (t) = tet cos 5t then L{f(t)} =?. 4s2 + 19s + 52 (b) if F (s) then L-1{F (s)} =? s (s2 + 4s…

Q: Question 3: A game of zumpie consists of 3 teams; 2 teams lose and 1 team wins. Fifty-one teams…

Q: QUESTION 2 The value of keid where b41 by using the two-point Gauss quadrature method of integrafion…

Q: Graph the function, considering the domain, critical points, symmetry, regions where the function is…

Q: 2: find fr. fy, and fz. a f(x, y. 2) = I+ xy- 22 2

A: Given f(x,y,z)=1+xy2-2z2 To find fx, fy, fz

Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

Q: C. Let A = {2, {2}, (V2)}, B = {2,{2}, {{2}}} and C = {2}. Write TRUE or FALSE on the space provided…

A: 1- FALSE 2-FALSE 3-FALSE

Q: We learnt in class/Notes that A[x] → (Vx)A[x] is NOT a theorem if x indeed occurs free in A. Yet, I…

Q: 4. For each equation of a surface given in spherical coordinates, sketch the surface and describe it…

Q: Use Stoke 's Theorem to evaluate [ V. dr, where v= y²i + xyj + xzk, and c is the bounding curve of…

Q: If A and B are 5 × 4 matrices, and C is a 3 x 5 matrix, which of the following are defined? OA. B+ A…

Q: Calculations for Finding E1(f) and E2(f) for Example 5.1. Compare the maximum error, average error,…

A: Here there are 8 data points so our N is 8 or our sample size is 8.

Q: Set A 1. Prove using vectors that the points (4, 3, 0), (2, 0, 1), (4, 1, -1), and (2, 2, 2) are the…

A: The given problem is to prove that the given vectors of points are the vertices of the rectangle and…

Q: 9:17 e dt 2/T الخيار 4 T/2 الخيار 2 II

Q: Find f(t). e s2 + 1

Q: I f is analytic and not Canstant in the Prinsple Q-2 interior of a region, then | f(2)l has no…

Q: b. A particle moves in simple harmonic motion according to the equation, s = A cos(wt) + B sin(wt).…

Q: Find all distinct eigenvalues of A. Then find the basic eigenvectors of A corresponding to each…

Q: Let there be the random vector Z E R"m Prove that E (||Z||) = tr(E[ZZ"]) %3D From the expression…

A: As per the question we are given a random m dimentional vector z , and we have to prove :…

Q: 1 The probability that I miss the bus to work on any day is 0.1.Whether I catch the bus on any day…

Q: Consider the initial value problem my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of…

A: Given my''+cy'+ky=Ft, y0=0, y'0=0 and m=2 kg, c=8 Kg/s, k=80 N/m and Ft=20if 0≤t≤π20if t>π2

Q: 3. We learned in class that for a given A, the f(r) that minimizes the cost function i=1 is a…

Q: If f {an} is a convergent sequence with lim an=0, n+ 00 then E=1ªn is a convergent series. True O…

Q: Solve y(4) y = cos t.

A: As per our guidelines we are supposed to answer only first one. Kindly repost other parts in the…

Q: You have 1000 bugs in a bottle. It is known that the bug population is given by the logistic model…

A: As per the question we are given a discrete logistic growth model of bugs. Then an antibiotic is…

Q: X = {r®};-1 = =1 = {23, 52, 29, 37, 46, 47, 25, 32, 49}. %3D (b) Execute the K-means algorithm with…

A: Here I run a python script to answer this question. Follow that.

Q: Let CR,t,,) be a Commutative ring ?

A: First I recall you Definition of commutative ring. A commutative ring is ring in which…

Q: 8. Let W be a subspace of a finite dimensional vector space V. Prove that there is a basis B for V…

Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: as per the rule we are authorized to provide the answer for only one question so please provide…

Q: Find the number of ways to colour faces of a cube using at most k colors, up to the group of…

A: First you enumerate the elements of the symmetry group of the cube. There are 24 of these, falling…

Q: Find the work Fdr done by the force F i+ yj+k around the curve C that is formed by the intersection…

Q: Find the amount applied to principle for the third month of a 4-year loan of $12,200 which charges…

Q: D. Write TRUE or FALSE on the space provided before each number. _6. x € {x, y, z} _7. x {{x}, {y},…

A: We have to check whether given statement is true or false.

Q: Find the area between r = 2-sin(θ) and r = sin(θ)

A: Area between polar curves

Q: 4X dy 2siny ?) S dy sinzx e 3) S sin? dx

Question

please answer this and show why they (a,b,c,d,e) are a subspace or not subspace

2. Determine which of the following is a subspace of R".
(a) {(x1,x2,..x,) | x1=0}
(b) {(x1, X2,.. , x,) | x1 2 0}
(c) {(x,X2...X)1 x 2x}
(d) {(x,X2..X) 1 =1-2x2}
(e) {(x, X2...x) | x = X2 == X,}
|3|

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

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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
Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
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=F,W=finF:f(x)=f(x)
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V= F, W=finF:f(0)=1
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.
My question is verifying how V5 is a subspace of R^5
Show that W = {(x1, x2): x1 ≥ 0 and x2 ≥ 0}, with the standard operations, is not a subspace of R2.
9. Show that P2 (polynomials of degree ≤ 2) is a subspace of P3 (polynomials of degree ≤ 3).
Suppose U and W are two-dimensional subspaces of R3. Show that U∩W≠{0}
Find a basis for the two-dimensional subspace of R^4 defined by