/*! 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} Q3E Do the polynomials f(t)=1+2t+9t2... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q3E (page 195)

Do the polynomials f(t)=1+2t+9t2+t3,g(t)=1+7t+7t3,h(t)=1+8t+t2+5t3,andk(t)=1+8t+4t2+8t3

form a basis ofP3?

Short Answer

Expert verified

The solution is the given polynomials forms the basis ofP3

Step by step solution

01

Definition for the linear independent.

If f is redundant if it is a linear combination off1,f2,...,fi-1then the elementsf1,f2,...,fnare linearly independent.

In this case the equation becomes

c1f1+c2f2+...+cnfn=0

Only has trivial solution

.c1=c2=....=cn=0

02

Solution for the polynomials of basis

Consider the given polynomial as follows

f(t)=1+2t+9t2+t3

g(t)=1+7t+7t3

h(t)=1+8t+t2+5t3

k(t)=1+8t+4t2+8t3

Here the simplification becomes as follows

f(t)+g(t)+h(t)+k(t)=(1+1+1+1)t3+(9+0+1+4)t2+(2+7+8+8)t+(1+1+1+1)鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�=4t3+14t2+25t+4

Since, the polynomial of the basis is of degree equal to 3.

Therefore, the given polynomial forms the basis of P3.

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

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

Find the transformation is linear and determine whether the transformation is an isomorphism.

T denotes the space of infinity sequence of real numbers, T(f(t))=[f7f11]fromP2toR2.

Which of the subsets Vof 鈩�3x3given in Exercise 6through 11are subspaces of鈩�3x3. The diagonal 3x3matrices.

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphism, T(ft)=F''(t)f(t) fromP2to P2.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

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.