/*! 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} Q1E TRUE OR FALSE?The polynomial of ... [FREE SOLUTION] | 魅影直播

魅影直播

Log out

Learning Materials

Features

Discover

Chapter 4: Q1E (page 199)

TRUE OR FALSE?

  1. The polynomial of degree less than 7 form a seven dimensional subspace of the linear space of all polynomials.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Definition of a polynomial.

A polynomial is the sum or difference of a collection of algebraic terms.

For example,

An algebraic expression of the form

anxn+an-1xn-1+......+a2x2+a1x+a0

  • Where all coefficientsare real numbers.
  • an鈮�0
  • The degreen is a non-negative integer.
02

Explanation for the given statement

Polynomials of degree less than seven form a spacep6 of all polynomials of degree six or less.

So, generally dimension of n+1 space of polynomials of degree 7 or less in n+1 to account for zero-degree polynomials.

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 魅影直播!

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 basis of all 2x2 lower triangular matrix, and determine its dimension.

Find a basis of a linear space and thus determine its dimension. Examine whether a subset of a linear space is a subspace. Which of the subsets of P2given in Exercises 1through 5are subspaces ofP2 (see Example 16)? Find a basis for those that are subspaces,{p(t):p(-t)=-p(t),forallt}.

Find the basis of all3脳3 upper triangular matrix, and determine its dimension.

Let V be the space of all infinite sequences of real numbers. See Example 5. Which of the subsets of given in Exercises 12 through 15 are subspaces of V ? The arithmetic sequences [i.e., sequences of the form(a,a+k,a+2k,a+3k,...) , for some constants and K .

a.Find the change of basis matrix S from the basis B considered in Exercise 24 to the standard basis U=(1,t,t2)of P2considered in Exercise 23.

b.Verify the formula SB = AS for the matrices B and A you found in Exercises 24 and 23,respectively.

c.Find the change of basis matrix from UtoB.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Discrete 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.