/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q63E If f1,f2,f3,f4,f5聽are elements ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q63E (page 201)

If f1,f2,f3,f4,f5are elements of a liner space V, and if there are exactly two redundant elements in the listf1,f2,f3,f4,f5, then there must be exactly two redundant elements in the listf2,f3,f4,f5as well.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Concept of redundant elements.

Consider the elementsf1,.....,fnin a linear space V.

Then is said to be redundant if it is a linear combinationoff1,....,fi - 1

02

Explanation of the solution.

Sincef1,f2,f3,f4,f5are elements of a linear space V.

And if there are exactly two redundant elements in the list f1,f2,f3,f4,f5then dim(V)=3.

The set of elements f1,f2,f3,f4,f5are same asf2,f3,f4,f5an order of elements of a set

does not make any difference.

Then there must be two redundant elements in the listf2,f3,f4,f5 as well.

Hence, the dimension of V is 3.

Thus, the statement is true.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

TRUE OR FALSE

6. if f1,..,fn is a basis of a linear space V, then any element of V can be written as a linear combination of f1,...,fn.

Let Vbe the space of all infinite sequences of real numbers. See Example 5. Which of the subsets ofgiven in Exercises 12 through 15 are subspaces of V? The geometric sequences [i.e., sequences of the form(a,ar,ar2,ar3,....), for some constantsand K.

In Exercise 72through 74, letZnbe the set of all polynomials of degree鈮�nsuch that f(0) = 0.

74. Define an isomorphism fromZntoPn-1(think calculus!).

Question: If T is a linear transformation from P6toP6that transformtk into a polynomial of degreek(fork=0,1,...,6) (for ) then T must be an isomorphism鈥�.

In Exercise 72through 74, letznbe the set of all polynomials of degree鈮�nsuch thatf(0)=0.

72. Show thatznis a subspace ofpnand find the dimension ofzn.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.