Question: Let f1(x),..., fn(x) be scalar functions. Suppose that every set of sample points x1, . . . ,xm R, for all finite m

Let f1(x),..., fn(x) be scalar functions. Suppose that every set of sample points x1, . . . ,xm ∈
R, for all finite m ≥ 1, leads to linearly dependent sample vectors f1.......fn ∈ Rm. Prove
that f1(x),..., fn(x) are linearly dependent functions.

Step by Step Solution

★★★★★

3.38 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Suppose the functions are linearly independent This means that for every 0 c c 1 ... 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)

952-M-L-A-E (1864).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Please help me how to do it... Thank You Forecast Your Demand \& Then Supply Demand Write a one-page summary of the purpose of moving average forecasting Create your company \& product, \& then a...

For n ¥ 1, let f n be real-valued measurable functions defined on an open set E R containing 0, and suppose that | f n ( x )| £ M (

For n ( 1, let fn be real-valued measurable functions defined on (, and suppose that |fn (x)| ( M ( for x ( (. Then for any sequence {xn} with it holds ( 0 a.e. [(], where ( is the Lebesgue measure? ...

Let E be a set in Rm. For each u: E R which has second-order partial derivatives on E, Laplace's equation is defined by a) Show that if u is C2 on E, then Îu = (u) on E. b) Show that if E R3...

Let x1, x2,. . . , xn be a distinct set of sample points. (a) Prove that the functions f1(x),... , fk(x) are linearly independent if their sample vectors f1......... f are linearly independent...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

Convex geometry 0.1 Dehn-Sommerville relations In this section we will talk about convex polytopes. One possible denition of a convex polytope uses the notion of a half-space: A closed half-space in...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

Least Squares Approximation Hector D. Ceniceros 1 Least Squares Approximation Let f be a continuous function on [a, b]. We would like to find the best approximation to f by a polynomial of degree at...

Compounds A and B are isomeric amines of molecular formula C8H11N. Identify each isomer on the basis of the 1H NMR spectra given in Figure 22.9.

How might the result in this case have been different if the court had admitted the Wagners evidence of the Love Song contract?

Multiple Choice What are the principal benefits of having a catastrophic health ir A To replace lost income during illness B To cover routine medical expenses C . To provide coverage for high - cost...

How do free cash flows and the weighted average cost of capital interact to determine a firms value? MINI CASE Assume that you recently graduated with a degree in finance and have just reported to...

The exposed surface (x = 0) of a plane wall of thermal conductivity k is subjected to microwave radiation that causes volumetric heating to vary as where q"0 (W/m3) is a constant. The boundary at x =...

What is conceptually the most defensible method for allocating support-department costs? Why?

Alternative methods of joint-cost allocation, ending inventories. The Darl Company operates a simple chemical process to convert a single material into three separate items, referred to here as X, 4...

Isooctane is produced in the reaction of isobutene and butylene in an emulsion with concentrated sulfuric acid: i-C 4 H 10 + C 4 H 8? ? i-C 8 H 18 The fresh feed to the process flows at a rate of...

Which of the eight market failures is the U.S. government least efective in correcting? Why do you think the U.S. government is particularly ineffective in this area?

Let A be a nonsingular matrix. Show that det(A-1) = 1 / det(A)

Show that if E is an elementary matrix then ET is an elementary matrix of the same type as E.

For each of the following, compute (i) det(A), (ii) adj A, and (iii) A-1. (a) (b) 2 110 100

15) Assume Jed Gerbil invested $ 13,891 into an account exactly two years ago. The account has an interest rate of 13.5 % p.a. How much does Jed have in his account today (that is, exactly two years...

Suresh buys a new car for $42000. He pays $3000 down and the rest in 48 monthly payments (at the end of each month). The interest rate is 4% compounded 12 times per year. (All answers to 2 decimal...

i need help asap Question 7 6 pts Julian Company sold goods for a total selling price of $9,500. The sale was made on account. The terms of the safe are 4/20./60. When Julian recorded this credit...