Question: (a) Show that a line t 0 through the origin of R3 is a subspace of R3. (b) Show that a line t in R3

(a) Show that a line t 0 through the origin of R3 is a subspace of R3.
(b) Show that a line t in R3 not passing through the origin is not a subspace of R3.

Step by Step Solution

★★★★★

3.46 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The line l 0 consists of all vectors of the fo... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

951-M-L-A-L-S (6934).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Given v ( 0 and p in, the line through p in the direction of v has the parametric equation x = p + t v. Show that a linear transformation T: maps this line onto another line or onto a single point (a...

Let L R2 be a line through the origin in the direction of the unit vector u. (a) Prove that the matrix representative of reflection through L is R = 2uuT - 1. (b) Find the corresponding formula for...

Let L be the line through the origin in R2 with direction vector = [a b]T 0. If PL denotes projection on L, show that PL has matrix 1 ab a +b ab b - u

6. Let S : {uh 11?, us, u4} be a set in R4. After performing the Gram-Schmidt process on S, v4 2 0, but v1 7E (1V; # 0, and V3 7E 0. Which oflhe following statements is true? (i mark) span(S)is a...

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2016 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

.2 e "-'-' h _ Delis ilion [-2 am or pl o In this part of the assignment, we will explore the idea of linear combinations and spans of vectors in R" that are testied in a particular way. Note that...

question below: x Let H = : 8x2 + 4y2 $1 , which represents the set of points on and inside an ellipse in the xy-plane. Find two Y specic examplestwo vectors, and a vector and a scalarto show that H...

Math 110 Homework Assignment 9 due date: Nov. 18, 2016 1. (a) Prove or disprove: the vectors ~v1 = (2, 3) and ~v2 = (1, 5) form a basis for R2 . (b) Prove or disprove: the vectors w ~ 1 = (1, 9) and...

In this exercise, you will be given two matrices A and B. You will write a set of commands in MATLAB that determine whether Row A and Row B are subspaces of the same space R". If yes, your code has...

In R^3, a line through the origin is the set of all points in R^3 whose coordinates satisfy x1 = at, x2 = bt, and x3 = ct, where t is a variable and a, b and c are not all zero. Show that a line...

Read the sentences below and decide the function of each sentence by specifying which states a claim and which states a support. Fill your answers in the blank boxes. Sentence Function It is often...

Given the circuit shown, answer the following questions I 40 8n 13 Vs 24/60 V VI j6n V22 -j4 n one of the following statements is correct: Choose... Choose... 12 in Ampere equals to: 2.65-j0.54 the...

Question 2 Match file descriptions for C ' s ADT implementations to their extensions ( client file excluded ) : should contain function definitions and a structure definitionMatch file descriptions...

You are the project manager for the KLN Project. You had 19 stakeholders on this project and have added 3 team members. How many more communication channels do you have now compared to before? A. 171...

Find values of x1 and x2 that minimize z = - 3x1 + 2x2 subject to 3x1 - x2 - 5 - x1 + x2 1 2x1 + 4x2 12 x1 0 x2 0

Solve the linear programming problem posed in Example 3.

A trucking firm ships the containers of two companies, A and B. Each container from company A weighs 40 pounds and is 2 cubic feet in volume. Each container from company B weighs 50 pounds and is 3...

Currency per U.S. $ Australia dollar 1.2372 6-months forward 1.2361 Japan Yen 100.2800 6-months forward 100.1000 U.K. Pound .6797 6-months forward .6776 Suppose interest rate parity holds, and the...

help quickly please Question 5 10 pts If the natural world is intrinsically valuable, then nature is considered valuable for its own sake. True O False Question 6 luck! iu questions and you have 30...

Hira Singh would like to purchase a condo in Phoenix. Her home is currently worth $ 6 8 9 , 0 0 0 . She has an existing mortgage with a balance owing of $ 2 5 0 , 0 0 0 , the condo in Phoenix is $ 1...