/*! 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} Q3E Find the rank of the matrices in... [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 1: Q3E (page 1)

Find the rank of the matrices in 2 through 4.
3. $[\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}]$

Short Answer

Expert verified

The rank of the matrix $[\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}]$ is, $1$ .

Step by step solution

01

Find row reduce echelon form

The number of leading 1鈥檚 in $rref (A)$ represents the rank of a matrix A denoted by $rank (A)$ .

The given matrix is, $[\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}]$ .

The reduced row echelon form of the given matrix is:

$r r e f [\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}] = [\begin{matrix} 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix}]$

02

Determine the rank of a matrix.

The number of leading 1鈥檚 in the matrix $[\begin{matrix} 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix}]$ are $1$ .

Hence, the rank of the given matrix is 1.

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

Compute the products Axin Exercises 13 through 15 using

paper and pencil. In each case, compute the product

two ways: in terms of the columns of A and in terms of the rows of A.

14.

$[\begin{matrix} 1 & 2 & 3 \\ 2 & 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 2 \\ 1 \end{matrix}]$

Consider the economy of Israel in 1958. The three industries considered here are

$\begin{array}{l} I_{1} : 鈥塧驳谤颈肠耻濒迟耻谤别, \\ I_{2} : 鈥尘补苍耻蹿补肠迟耻谤颈苍驳, \\ I_{3} : 鈥塭苍别谤驳测 \end{array}$

Outputs and demands are measured in millions of Israeli pounds, the currency of Israel at that time. We are told that

$\begin{array}{l} \overset{鈫�}{b} = [\begin{matrix} 13 .2 \\ 17 .6 \\ 1 .8 \end{matrix}], \overset{鈫�}{蠀_{1}} = [\begin{matrix} 0 .293 \\ 0 .014 \\ 0 .044 \end{matrix}], \\ \overset{鈫�}{蠀_{2}} = [\begin{matrix} 0 \\ 0 .207 \\ 0 .01 \end{matrix}], \overset{鈫�}{蠀_{3}} = [\begin{matrix} 0 \\ 0 .017 \\ 0 .216 \end{matrix}] \end{array}$

a. Why do the first components of $\overset{鈫�}{蠀_{2}}$ and $\overset{鈫�}{蠀_{3}}$ equal $0$ ?

b. Find the outputs $x_{1}$ , $x_{2}$ , $x_{3}$ required to satisfy demand.

In exercises, 1 through 10, find all solutions of the linear systems using elimination.Then check your solutions.

9. $|x + 2 y + 3 z = 1 3 x + 2 y + z = 1 7 x + 2 y - 3 z = 1|$

If Ais a symmetric nxnmatrix such that $A^{n} = 0$ , then Amust be the zero matrix.

If the determinants of all the principal submatrices of a symmetric 3X3matrixare negative, thenmust be negative definite.

See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

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.