/*! 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} Q18E If a linear space V聽can be span... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q18E (page 199)

If a linear space Vcan be spanned by 10elements, then the dimension of Vmust be.猢�10

Short Answer

Expert verified

The statement is True

Step by step solution

01

Determine the dimension of V .

Consider the a set V that is spanned by 10 elements.

An element Eis spanned by the setx1,x2,...,xn if there exist the constantsuch thatE=a1x1+a2x2+...+anxn.

The dimension of a set Dis defined as the total number of linear independent set that span any element of the set.

02

Determine whether the statement is True or False

If every element of V is linear independent then by the definition the dimension of the set V is 10.

Therefore, the dimension of the set V is 猢�10.

Hence, 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

Find the transformation is linear and determine whether they are isomorphism.

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphism, T(f(t))=f(7) fromP2torole="math" localid="1659412169328" 鈩�.

T denotes the space of infinity sequence of real numbers,T(f(t))=f(t2)from PtoP.

In Exercises 5 through 40, find the matrix of the given linear transformation Twith respect to the given basis. If no basis is specified, use standard basis:渭=(1,t,t)forP2,

渭=([1000],[0100],[0010],[0001])

for鈩�2脳2and渭=(1,i)for,鈩�2脳2.For the spaceU2脳2of upper triangular2脳2matrices, use the basis

渭=([1000],[0100],[0001])

Unless another basis is given. In each case, determine whetherTis an isomorphism. IfTisn鈥檛 an isomorphism, find bases of the kernel and image ofTand thus determine the rank ofT.

17.T(z)=izfromCtoCwith respect to the basisB={1,i}.

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphism,T(x+iy)=x2+y2 from 鈩�to 鈩�.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

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.