/*! 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 Sketch the image of the standard... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q1E (page 71)

Sketch the image of the standard L under the linear transformation

T(x鈫�)=[3112]x鈫�

See Example 1.

Short Answer

Expert verified

The image consists of vectors31,24.

Step by step solution

01

Step1:Linear transformation

We have given T is linear transformation with

T(x鈫�)=3112x鈫�

.

Vectors for L shape are10,02.

Apply the given transformation on10,02.

For sketching the image of transformations, we will do this by

T10=311210=31

T02=311202=24

02

Sketching the image 

03

Description of image

In the image of this linear transformation, it is rotated by angle in the clockwise direction.

And the vertical is rotated by Angle in an anticlockwise direction.

The image consists of vectors are31,24.

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

There exists an invertible 2 脳 2 matrix A such that A-1=[1111].

In this exercise we will verify part (b) of Theorem 2.3.11 in the special case when A is the transition matrix [0.40.30.60.7]andx炉is the distribution vector[10]. [We will not be using parts (a) and (c) of Theorem 2.3.11]. The general proof of Theorem 2.3.11 runs along similar lines, as we will see in Chapter 7.

  1. ComputeA[12]andA[1-1]. WriteA[1-1]as a scalar multiple of the vector[1-1].
  2. Write the distribution vectorx鈫�=[10]as a linear combination of the vectors[12]and[1-1]
  3. Use your answers in part (a) and (b) to writeAx鈫�as a linear combination of the vectors[12]and[1-1]. More generally, write Amx鈫�as a linear combination of vectors[12]and[1-1], for any positive integer m. See Exercise 81.
  4. In your equation in part (c), let got to infinity to find limm鈫�鈭�Amx鈫�. Verify that your answer is the equilibrium distribution for A.

TRUE OR FALSE?

If a matrixA=(abcd) represents the orthogonal projection onto a line L , then the equationa2+b2+c2+d2=1must hold.

TRUE OR FALSE?

The functionT[xy]=[y+12y-12x-32x+32] is a linear transformation.

The conversion formula C=59(F-32) from Fahrenheit to Celsius (as measures of temperature) is nonlinear, in the sense of linear algebra (why?). Still, there is a technique that allows us to use a matrix to represent this conversion.

a. Find the 2脳2 matrixAthat transforms the vector [F1] into the vector [C1]. (The second row of A will be [01].)

b. Is the matrix Ain part (a) invertible? If so, find the inverse (use Exercise 13). Use the result to write a formula expressing F in terms of C

See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.