/*! 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} Q5E Consider the linear transformati... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q5E (page 53)

Consider the linear transformation T from R3 to R2with

T010=69andT001=-1317

Find the matrixAofT .

Short Answer

Expert verified

Matrix representation of given transformation isA=96-1311917 .

Step by step solution

01

Step1: System of equation

We have given the T is linear transformation with

T100=711,T010=69,T001=-1317

02

Linear Transformation  

Let any vectora=(x1,x2,x3)鈭�R3 .

Now, since T is linear transformation.

T(x1,x2,x3)=x1T(1,0,0)+x2T(0,1,0)+x3T(0,0,1)T(x1,x2,x3)=x1(7,11)+x2(6,9)+x3(-13,17)T(x1,x2,x3)=(7x1,11x1)+(6x2,9x2)+(-13x3,17x3)T(x1,x2,x3)=(7x1+6x2-13x3)+(11x1,9x2,17x3)

03

Matrix for linear transformation

The matrix representation of T by2脳3 matrix A.

A=76-1311917

.

Hence, the matrix representation Matrix representation of given transformation isA=76-1311917 .

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?

There exists a real number k such that the matrix [k-23-3k-2]fails to be invertible.

Let A=[110-312]in all parts of this problem.

(a) Find the scalar位 such that the matrixA-位濒2fails to be invertible. There are two solutions; choose one and use it in parts (b) and (c).

(b) For the 位you choose in part (a), find a non-zero vector x鈬赌such that

role="math" localid="1659697491583" (A-位濒2)x鈬赌=0鈬赌

(c) Note that the equation (A-位濒2)x鈬赌=0鈬赌can be written as.

A-位x鈬赌=0鈬赌orAx鈬赌=位x鈬赌Check that the equationAx鈬赌=位x鈬赌 holds for your位from part (a) and yourx鈬赌from part (b).

If A and B are two 4 脳 3 matrices such thatAv鈫�=Bv鈫� for all vectorsv鈫� in鈩�3 , then matrices A and B must be equal.

Question:

  1. If Ais any 3x3 transition matrix (see Definition 2.1.4), find the matrix product [111]A .
  2. For a fixed n , let e鈫� be the row vector e鈫�=[1,1,..,1]n1's . Show that an nxn matrix A with nonnegative entries is a transition matrixif (and only if)e鈫�A=e鈫� .

For which values of the constant k is the following matrix invertible?

[11112k14k2]
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.