/*! 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} Q18E The linear transform T(x鈫�)=[0.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q18E (page 72)

The linear transform T(x鈫�)=[0.60.80.8鈭�0.6]x鈫�is a reflection about a line L. See Exercise 17. Find the equation of line L (in the form y=mx).

Short Answer

Expert verified

The equation of the line is,y=12x.

Step by step solution

01

Compute the matrix

Consider the matrix

T(x鈫�)=0.60.80.8鈭�0.6x鈫�

As A(蠀鈫�)=蠀鈫�,

Thus,0.60.80.8鈭�0.6蠀1蠀2=蠀1蠀2

02

Compute the vector components

Represent the matrix in terms of equations.

0.6蠀1+0.8蠀2=蠀10.8蠀1鈭�0.6蠀2=蠀2

Consider any one equation.

0.8蠀2=蠀1鈭�0.6蠀1鈬�0.8蠀2=0.4蠀1鈬�蠀2蠀1=0.40.8

03

Compute the slope and the equation of the line

The slope of the line equals the second over first component of the vector.

蠀2蠀1=0.40.8鈬�m=0.40.8鈭�m=12

Thus, the equation of the line L in terms of y=mx+cis,y=12x.

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

Use the concept of a linear transformation in terms of the formula y=Ax鈬赌, and interpret simple linear transformations geometrically. Find the inverse of a linear transformation from localid="1659964769815" 鈩�2to鈩�2to (if it exists). Find the matrix of a linear transformation column by column.

Consider the transformations from鈩�3to鈩�3defined in Exercises 1 through 3. Which of these transformations are linear?

  1. y1=2x2y2=x2+2y3=2x2

TRUE OR FALSE?

There exists a real number k such that the matrix[k-1-2-4k-3] fails to be invertible.

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation T(x)鈫�=Ax鈫�on this face.

25. [2002]

TRUE OR FALSE?

If A2=In, then matrixAmust be invertible.

TRUE OR FALSE?

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

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

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.