Question: Let V be a vector space and let X, X2, X3, , Y2 EV. Suppose that both the list X, X2, X3, and the

Let V be a vector space and let x1, X2, X3 , y1, y2 E V. Suppose that both the list x1, x2, X3 , and the list y1, y2 are line

Let V be a vector space and let X, X2, X3, , Y2 EV. Suppose that both the list X, X2, X3, and the list y, y are linearly independent. Prove that the list X, X2, X3, , is linearly independent iff span{X, X2, X3} span{y, } = {0}.

Step by Step Solution

★★★★★

3.46 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To prove that the list mathbfx1 mathbfx2 mathbfx3 mathbfy1 mathbfy2 is linearly independent if and only if textspan mathbfx1 mathbfx2 mathbfx3 cap tex... 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

Students Have Also Explored These Related Mathematics Questions!

Let V be a vector space and let x V. Show that: (a) 0 = 0 for each scalar . (b) If x = 0, then either = 0 or x = 0.

Let V be a vector space and assume that the maps f1, f2: V R1 are linear. (a) Define a map F: V R2 whose component functions are the given linear ones. Show that F is linear. (b) Does the converse...

Let V be a vector space with a basis B = {b1, ....bn) Let W be the same space V with a basis C = {c1,... c2) be the identity transformation I : V W. Find the matrix for I relative to B and C. What...

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

Ryan Ren Assignment Homework 2 due 09/14/2017 at 02:15pm PDT 1. (1 pt) Compute the following product. \u0014 \u0015\u0014 \u0015 \u0014 5 0 4 7 4 = 0 7 1 7 7 Math4A-02-M17-Wen \u0015 Answer(s)...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Can you please help me with number 21. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! Open with Chapter 5 Linear Systems...

Math 110 Homework Assignment 22 due date: Mar. 31, 2017 1. In each of the following cases, either prove that the given subset W is a subspace of V , or show why it is not a subspace of V . (a) V = C...

Why is there a depletion layer in the immediate vicinity of the junction? 1 [TURN OVER CST.93.1.2 SECTION B 5 Give an ML definition of the function map3 which has the property that map3 f [x1, x2, ....

Suppose that R(A, B, C) is a relational schema with functional dependencies F = {A, B C, C B}. (i) Is this schema in 3NF? Explain. [2 marks] (ii) Is this schema in BCNF? Explain. [2 marks] (b)...

Find the Fourier series of f(x) = x + x in (-, n)

Poynton Carpets Ltd sells floor coverings and runs a small fleet of vans for the firms carpet fitters. The vans are depreciated on the straight-line basis over 4 years to a standard residual value of...

Which of the following is an example of a general partnership? Ken and Paul start a graphic design business together. When Ken falls to deliver on a contract with a customer, Ken and Paul are held...

Ajax Company had a $17,000, 7%, 30-day note of Beatrice Inc. At maturity, April 4, Beatrice dishonoured the note. Record the entry on April 4.

On August 2, 2014, SLM Company received a $5,500, 90-day, 5% notes from customer Will Carr as payment on his account. Determine the maturity date and prepare the August 2 and maturity date entries,...

Winston Abbott operates Abbott Small Engine Repair on his cattle farm, greatly supplementing his farm income. Most of his customers pay cash, so he uses the direct write-off method to account for...

Omer is part of the management team of a Canadian public company and is eligible for the employee stock option plan. A few years ago he received an option on 1,000 shares. The current price of the...

Trent Zalinski recently retired as a football player with the Saskatchewan Roughriders. In the current year, he received his salary of $150,000 from the team and is eligible for a CFL pension in 15...

If reserves in the banking system increase by $100, then chequable deposits will increase by $1000 in the simple model of deposit creation when the desired reserve ratio is ________. Question 34...

1. Fill in the blanks. Consider the following vector v from (0, 0) to (a,b). v = ai + bj The horizontal component of v is The vertical component of v is _ The magnitude of v is given by | vl| =_ The...

1. Fill in the blanks. Consider the following vector v from (0, 0) to (a,b). v = ai + bj The horizontal component of v is _. The vertical component of v is _. The magnitude of v is given by The...

8.4 Write on paper for upvote please. Questions: 12, 17, 22 8.4 Matrices for General Linear Transformations 485 b. Verify that Formula (8) holds for every vector in R'. d. Use the formula obtained in...

,, kindly solve Consider the Linear Regression Model 1. For any X = x, let Y = x8 + U, where B E R*. 2. X is exogenous. 3. The probability model is { f (u; ) is a distribution on R : E, [U] = 0, Var,...

,. solve the following Consider the following models describing the relationship between monthly return on the Standard & Poor's 500 stock market index (rsp500), the re- turn on three-month T-bills...

1. Determine which of the following sets form a basis of the respective vector spaces and justify your answer: (a) {4t 2t+3,6t t +4, 8t - 8t+7} of P2(R), the vector space of polynomials in t - over R...