/*! 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} Q17E Find the determinants of the lin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q17E (page 289)

Find the determinants of the linear transformations in Exercises 17 through 28.

17.T(f)=2f+3f'fromP2toP2

Short Answer

Expert verified

Therefore, the determinant of the linear transformations is given by,

det T = det B = 8 .

Step by step solution

01

Definition

A determinant is a unique number associatedwith a square matrix.

A determinant is a scalar value that is a function of the entries of a square matrix.

It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.

02

Given

Given linear transformation,

T(f)=2f+3f'fromP2toP2

03

To find determinant

Forf鈭�P2we haveft=at2+bt+c. So we compute

Tft=2ft+3f'tTft=2at2+bt+c+32at+bTft=2at2+(6a+2b)t+(3b+2c)

Since B=t2,t,1is a basis for P2, the matrix of T corresponding to B is

B=200620032

Therefore,

det T =det B = 8.

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

Consider those 4脳4matrices whose entries are all 1 , -1 , or 0 . What is the maximal value of the determinant of a matrix of this type? Give an example of a matrix whose determinant has this maximal value.

Consider a 4x4 matrix A with rows V1鈫�,V2鈫�,V3鈫�,V4鈫�. If det(A) = 8, find the determinants in Exercises 11 through 16.

16. role="math" localid="1659506283449" det[6v鈬赌1+2v鈬赌4v鈬赌2v鈬赌33v鈬赌1+v鈬赌4]

IfA is a 4脳4 matrix whose entries are all 1 or -1 , then detAmust be divisible by 8 (i.e., detA=8kfor some integer k).

Find all 2x2matrices for which [23]is an eigenvector with associated eigenvalue -1.

Question: Let A and B be 2 x 2 matrices with integer entries such that A,A+B,A+2B,A+3B, and A+4B are all invertible matrices whose inverses have integer entries. Show that A+5B is invertible and that it鈥檚 inverse has integer entries. This question was in the William Lowell Putnam Mathematical Competition in 1994. Hint: Consider the function F(t)=(det(A+tB))2 -1. Shows that this is a polynomial; what can you say about its degree? Find the values f(0), f(1), f(2), f(3), f(4),using Exercise 53. Now you can determine f(t) by using a familiar result: If a polynomial f(t) of degree <m has more than m zeros, then f(t)=0 for all t.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.