/*! 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} Q30E There exists an invertible 2 脳 ... [FREE SOLUTION] | 91影视

91影视

Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology
Features
Features

Discover all of these amazing features with a free account.

Flashcards

91影视 AI

Notes

Study Plans

Study Sets
What鈥檚 new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
91影视
Discover

All the hacks around your studies and career - in one place.

Find a degree

Magazine
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

The largest student job board with the most exciting opportunities.

Verified student deals from top brands.

Discover our mobile app to take your studies anywhere.

Learning Materials

Features

Discover

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 2: Q30E (page 108)

There exists an invertible 2 脳 2 matrix A such that $A^{- 1} = [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}]$ .

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Explaining

The claim is that there exists an invertible 2x2 matrix A such that $A^{- 1} = [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}]$ . If $A^{- 1} = [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}]$ then: $A = {(A^{- 1})}^{- 1}$

$A^{- 1} = {[\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}]}^{- 1}$

Now we know that $[\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}]$ is invertible as long as $d e t [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}] 鈮� 0$

02

Conclusion

If we calculate $d e t [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}]$ we have $d e t [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}] = 1 - 1 = 0$ .

Thus the inverse does not exist and the statement is false.

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

Give a geometric interpretation of the linear transformations defined by the matrices in Exercises $16$ through $23$ . Show the effect of these transformations on the letter $L$ considered in Example $5$ . In each case, decide whether the transformation is invertible. Find the inverse if it exists, and interpret it geometrically. See Exercise $13$

$[\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}]$

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 $T \overset{鈫�}{(x)} = A \overset{鈫�}{x}$ on this face.

26. $[\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]$

Let Lbe the line in $R^{3}$ that consists of all scalar multiples of $[\begin{array}{l} 2 \\ 1 \\ 2 \end{array}]$ . Find the orthogonal projection of the vector $[\begin{array}{l} 1 \\ 1 \\ 1 \end{array}]$ onto line L.

When you represent a three 鈥揹imensional object graphically in the plane (on paper, the blackboard, or a computer screen), you have to transform spatial coordinates,

$[\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}]$ ,

Into plane coordinates, $[\begin{matrix} y_{1} \\ y_{2} \end{matrix}]$ . The simplest choice is a linear transformation, for example, the one given by the matrix

$[\begin{matrix} - \frac{1}{2} & 1 & 0 \\ - \frac{1}{2} & 0 & 1 \end{matrix}]$

(a.) Use this transformation to represent the unit cube with corner points

$[\begin{matrix} 0 \\ 0 \\ 0 \end{matrix}], [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}], [\begin{matrix} 0 \\ 1 \\ 0 \end{matrix}], [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}], [\begin{matrix} 1 \\ 1 \\ 0 \end{matrix}], [\begin{matrix} 0 \\ 1 \\ 1 \end{matrix}], [\begin{matrix} 1 \\ 0 \\ 1 \end{matrix}], [\begin{matrix} 1 \\ 1 \\ 1 \end{matrix}]$

Include the images of the axes in your sketch:

(b) Represent the image of the point $[\begin{matrix} 1 \\ \frac{1}{2} \\ \frac{1}{2} \end{matrix}]$ in your figure in part (a)

(c.) Find all the points $[\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}]$ in ${鈩�}^{3}$ that are transformed to $[\begin{matrix} 0 \\ 0 \end{matrix}]$ . Explain.

Consider the transformation T from $R^{2}$ to $R^{2}$ that rotates any vector $\overset{鈫�}{x}$ through an angle of $45 掳$ in the counterclockwise direction, as shown in the following figure:

You are told that T is a linear transformation. (This will be shown in the next section.) Find the matrix of T .

See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

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.