Skip to main content

Math Algebra EBK DIFFERENTIAL EQUATIONS AND LINEAR A

Let A = [ 1 2 4 3 1 6 k 3 2 ] . a) In terms of k , find the volume of the parallelepiped determined by the row vectors of the matrix A . b) Does your answer to (a) change if we instead consider the volume of the parallelepiped determined by the column vectors of the matrix A ? Why or why not? c) For what value(s) of k , if any, is A invertible.

Let A = [ 1 2 4 3 1 6 k 3 2 ] . a) In terms of k , find the volume of the parallelepiped determined by the row vectors of the matrix A . b) Does your answer to (a) change if we instead consider the volume of the parallelepiped determined by the column vectors of the matrix A ? Why or why not? c) For what value(s) of k , if any, is A invertible.

Solution Summary: The author explains the volume of the parallelepiped in terms of k determined by row vectors of matrix A and comparing answer with part(a).

EBK DIFFERENTIAL EQUATIONS AND LINEAR A

EBK DIFFERENTIAL EQUATIONS AND LINEAR A

4th Edition

ISBN: 8220102019799

Author: ANNIN

Publisher: YUZU

See similar textbooks

Concept explainers

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

Videos

Textbook Question

Chapter 3.2, Problem 46P

Let A = [ 1 2 4 3 1 6 k 3 2 ] .

a) In terms of k , find the volume of the parallelepiped determined by the row vectors of the matrix A .

b) Does your answer to (a) change if we instead consider the volume of the parallelepiped determined by the column vectors of the matrix A ? Why or why not?

c) For what value(s) of k , if any, is A invertible.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

Blurred answer

Chapter 3.2, Problem 45P

Chapter 3.2, Problem 47P

Chapter 3 Solutions

EBK DIFFERENTIAL EQUATIONS AND LINEAR A

Ch. 3.1 - True-False Review For items (a)(j), decide if the...Ch. 3.1 - True-False Review For items (a)(j), decide if the...Ch. 3.1 - True-False Review For items a-j, decide if the...Ch. 3.1 - For Problems 1-6, determine the number of...Ch. 3.1 - For Problems 1-6, determine the number of...Ch. 3.1 - For Problems 1-6, determine the number of...Ch. 3.1 - For Problems 1-6, determine the number of...Ch. 3.1 - Prob. 5P Ch. 3.1 - Prob. 6P Ch. 3.1 - Use Definition 3.1.8 to derive the general...

Ch. 3.1 - Prob. 11P Ch. 3.1 - For Problems 1215, determine the values of the...Ch. 3.1 - Prob. 13P Ch. 3.1 - Prob. 14P Ch. 3.1 - For Problems 1215, determine the values of the...Ch. 3.1 - Prob. 16P Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 18P Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 20P Ch. 3.1 - Prob. 21P Ch. 3.1 - Prob. 22P Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 24P Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 26P Ch. 3.1 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - Prob. 29P Ch. 3.1 - Prob. 30P Ch. 3.1 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - Prob. 36P Ch. 3.1 - Prob. 37P Ch. 3.1 - Prob. 38P Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 42P Ch. 3.1 - For Problems 43-46, evaluate the determinant of...Ch. 3.1 - For Problems 43-46, evaluate the determinant of...Ch. 3.1 - Prob. 45P Ch. 3.1 - Prob. 46P Ch. 3.1 - In Problem 4748, we explore a relationship between...Ch. 3.1 - Prob. 48P Ch. 3.1 - (a) Write all 24 distinct permutations of the...Ch. 3.1 - Prob. 50P Ch. 3.1 - Prob. 52P Ch. 3.1 - 3.1Problems a) If A=[a11a12a21a22] and c is a...Ch. 3.1 - Prob. 55P Ch. 3.1 - Prob. 56P Ch. 3.1 - Let A be an arbitrary 44 matrix. By experimenting...Ch. 3.1 - Prob. 59P Ch. 3.2 - For items a-f, decide if the given statement is...Ch. 3.2 - Prob. 2TFR Ch. 3.2 - For items a-f, decide if the given statement is...Ch. 3.2 - Prob. 4TFR Ch. 3.2 - Prob. 5TFR Ch. 3.2 - Prob. 6TFR Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 8P Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 10P Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 12P Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 14P Ch. 3.2 - For Problems 1521, use Theorem 3.2.5 to determine...Ch. 3.2 - Prob. 16P Ch. 3.2 - For Problems 1521, use Theorem 3.2.5 to determine...Ch. 3.2 - Prob. 18P Ch. 3.2 - Prob. 19P Ch. 3.2 - Prob. 20P Ch. 3.2 - For Problems 1521, use Theorem 3.2.5 to determine...Ch. 3.2 - Prob. 22P Ch. 3.2 - Determine all values of the constant k for which...Ch. 3.2 - Determine all values of the constant k for which...Ch. 3.2 - Determine all values of the constant k for which...Ch. 3.2 - If A=[112314013], find det(A), and use properties...Ch. 3.2 - Prob. 27P Ch. 3.2 - Verify property P9 for the matrices...Ch. 3.2 - For Problems 2932, let A=[abcd] and assume...Ch. 3.2 - For Problems 2932, let A=[abcd] and assume...Ch. 3.2 - Prob. 31P Ch. 3.2 - Prob. 32P Ch. 3.2 - For Problems 33-36, let A=[abcdefghi] and assume...Ch. 3.2 - For Problems 33-36, let A=[abcdefghi] and assume...Ch. 3.2 - For Problems 33-36, let A=[abcdefghi] and assume...Ch. 3.2 - Prob. 36P Ch. 3.2 - For Problems 37-44, let A and B be 44 matrices...Ch. 3.2 - For Problems 37-44, let A and B be 44 matrices...Ch. 3.2 - For Problems 37-44, let A and B be 44 matrices...Ch. 3.2 - For Problems 37-44, let A and B be 44 matrices...Ch. 3.2 - For Problems 37-44, let A and B be 44 matrices...Ch. 3.2 - For Problems 37-44, let A and B be 44 matrices...Ch. 3.2 - For Problems 37-44, let A and B be 44 matrices...Ch. 3.2 - For Problems 37-44, let A and B be 44 matrices...Ch. 3.2 - Let A,B,andS be nn matrices. If S1AS=B, must A=B?...Ch. 3.2 - Let A=[124316k32]. a) In terms of k, find the...Ch. 3.2 - Without expanding the determinant, determine all...Ch. 3.2 - Use only properties P1,P2,P6 to show that...Ch. 3.2 - Prob. 49P Ch. 3.2 - Prob. 50P Ch. 3.2 - An nn matrix A that satisfies AT=A1 is called an...Ch. 3.2 - a. Use the definition of a determinant to prove...Ch. 3.2 - Use the determinants to prove that if A is...Ch. 3.2 - If A and S are nn matrices with S invertible, show...Ch. 3.2 - Prob. 55P Ch. 3.2 - Let E be an elemetary matrix. Verify the formula...Ch. 3.2 - Show that |xy1x1y11x2y21|=0 represents the...Ch. 3.2 - Without expanding the determinant, show that...Ch. 3.2 - If A is an nn skew symmetric matrix and n is odd,...Ch. 3.2 - Prob. 60P Ch. 3.2 - Let A be general 44 matrix. a Verify property P1...Ch. 3.2 - Prob. 62P Ch. 3.2 - Determine all values of a for which...Ch. 3.2 - Prob. 64P Ch. 3.2 - Prob. 65P Ch. 3.3 - For items (a)(j), decide if the given statement is...Ch. 3.3 - For items (a)(j), decide if the given statement is...Ch. 3.3 - Prob. 5TFR Ch. 3.3 - Prob. 6TFR Ch. 3.3 - Prob. 7TFR Ch. 3.3 - Prob. 8TFR Ch. 3.3 - Prob. 9TFR Ch. 3.3 - Prob. 1P Ch. 3.3 - Prob. 2P Ch. 3.3 - For Problems 1-4, determine all minors and...Ch. 3.3 - Prob. 4P Ch. 3.3 - Prob. 5P Ch. 3.3 - Prob. 6P Ch. 3.3 - Prob. 7P Ch. 3.3 - Prob. 8P Ch. 3.3 - For Problems 7-14, use the cofactor expansion...Ch. 3.3 - Prob. 10P Ch. 3.3 - Prob. 11P Ch. 3.3 - For Problems 7-14, Use the cofactor expansion...Ch. 3.3 - Use the cofactor expansion theorem to evaluate the...Ch. 3.3 - Prob. 14P Ch. 3.3 - For Problems 1522, evaluate the given determinant...Ch. 3.3 - Prob. 16P Ch. 3.3 - Prob. 17P Ch. 3.3 - Prob. 18P Ch. 3.3 - Prob. 19P Ch. 3.3 - For Problems 1522, evaluate the given determinant...Ch. 3.3 - For Problems 1522, evaluate the given determinant...Ch. 3.3 - Prob. 22P Ch. 3.3 - Prob. 23P Ch. 3.3 - Prob. 24P Ch. 3.3 - Prob. 25P Ch. 3.3 - Prob. 26P Ch. 3.3 - Prob. 27P Ch. 3.3 - Prob. 28P Ch. 3.3 - Prob. 29P Ch. 3.3 - Prob. 30P Ch. 3.3 - Prob. 31P Ch. 3.3 - For Problems 3138, determine the eigenvalues of...Ch. 3.3 - For Problems 3138, determine the eigenvalues of...Ch. 3.3 - For Problems 3138, determine the eigenvalues of...Ch. 3.3 - For Problems 3138, determine the eigenvalues of...Ch. 3.3 - For Problems 3138, determine the eigenvalues of...Ch. 3.3 - Prob. 37P Ch. 3.3 - Prob. 39P Ch. 3.3 - Prob. 40P Ch. 3.3 - Prob. 41P Ch. 3.3 - Prob. 42P Ch. 3.3 - Prob. 43P Ch. 3.3 - Prob. 44P Ch. 3.3 - Prob. 45P Ch. 3.3 - Prob. 46P Ch. 3.3 - Prob. 47P Ch. 3.3 - Prob. 48P Ch. 3.3 - Prob. 49P Ch. 3.3 - Prob. 50P Ch. 3.3 - Prob. 51P Ch. 3.3 - Prob. 52P Ch. 3.3 - Prob. 53P Ch. 3.3 - Prob. 54P Ch. 3.3 - Prob. 55P Ch. 3.3 - Prob. 57P Ch. 3.3 - Prob. 58P Ch. 3.3 - Prob. 59P Ch. 3.3 - Prob. 60P Ch. 3.3 - For Problems 59-64, use Cramers rule to solve the...Ch. 3.3 - Prob. 62P Ch. 3.3 - Prob. 63P Ch. 3.3 - Prob. 64P Ch. 3.3 - Prob. 65P Ch. 3.3 - Prob. 66P Ch. 3.3 - Prob. 67P Ch. 3.3 - Prob. 68P Ch. 3.3 - Prob. 69P Ch. 3.3 - Let A be a randomly generated invertible 44...Ch. 3.3 - Prob. 72P Ch. 3.4 - For Problems 1-8, evaluate the given determinant....Ch. 3.4 - For Problem 1-8, evaluate the given determinant....Ch. 3.4 - For Problem 1-8, evaluate the given determinant....Ch. 3.4 - For Problem 1-8, evaluate the given determinant....Ch. 3.4 - For Problem 1-8, evaluate the given determinant....Ch. 3.4 - Prob. 6P Ch. 3.4 - For Problem 1-8, evaluate the given determinant....Ch. 3.4 - For Problem 1-8, evaluate the given determinant....Ch. 3.4 - Prob. 9P Ch. 3.4 - Prob. 10P Ch. 3.4 - Prob. 11P Ch. 3.4 - For problems 9-14, find det(A). If A is...Ch. 3.4 - Prob. 13P Ch. 3.4 - For problems 9-14, find det(A). If A is...Ch. 3.4 - Prob. 15P Ch. 3.4 - Prob. 16P Ch. 3.4 - For Problems 15-20, use Cramers rule to determine...Ch. 3.4 - Prob. 18P Ch. 3.4 - For Problems 15-20, use Cramers rule to determine...Ch. 3.4 - Prob. 20P Ch. 3.4 - Prob. 21P Ch. 3.4 - Prob. 22P Ch. 3.4 - Prob. 23P Ch. 3.4 - For Problems 23-29, assume that A and B be 33...Ch. 3.4 - Prob. 25P Ch. 3.4 - Prob. 26P Ch. 3.4 - For Problems 23-29, assume that A and B be 33...Ch. 3.4 - For Problems 23-29, assume that A and B be 33...Ch. 3.4 - Prob. 29P Ch. 3.5 - For Problems 1-6, evaluate the determinant of the...Ch. 3.5 - For Problems 1-6, evaluate the determinant of the...Ch. 3.5 - For Problems 1-6, evaluate the determinant of the...Ch. 3.5 - For Problems 1-6, evaluate the determinant of the...Ch. 3.5 - For Problems 16, evaluate the determinant of the...Ch. 3.5 - Prob. 6AP Ch. 3.5 - Prob. 7AP Ch. 3.5 - Prob. 8AP Ch. 3.5 - Prob. 9AP Ch. 3.5 - Prob. 10AP Ch. 3.5 - For Problem 11-14, suppose A and B are 44...Ch. 3.5 - For Problem 11-14, suppose A and B are 44...Ch. 3.5 - Prob. 13AP Ch. 3.5 - Prob. 14AP Ch. 3.5 - Prob. 15AP Ch. 3.5 - Prob. 16AP Ch. 3.5 - Prob. 17AP Ch. 3.5 - Prob. 18AP Ch. 3.5 - Prob. 19AP Ch. 3.5 - Prob. 20AP Ch. 3.5 - Prob. 21AP Ch. 3.5 - Prob. 22AP Ch. 3.5 - Prob. 23AP Ch. 3.5 - Prob. 24AP Ch. 3.5 - Prob. 25AP Ch. 3.5 - Prob. 26AP Ch. 3.5 - Prob. 27AP Ch. 3.5 - Prob. 28AP Ch. 3.5 - Prob. 29AP Ch. 3.5 - Prob. 30AP Ch. 3.5 - Prob. 31AP Ch. 3.5 - Prob. 32AP Ch. 3.5 - Prob. 33AP Ch. 3.5 - True or false: Given any real number r and any 33...Ch. 3.5 - Prob. 35AP Ch. 3.5 - Prob. 36AP Ch. 3.5 - Prob. 37AP Ch. 3.5 - Let A and B be nn matrices such that AB=BA. Use...Ch. 3.5 - A real nn matrix A is called orthogonal if...Ch. 3.5 - For Problems 40-42, Use Cramers rule to solve the...Ch. 3.5 - For Problems 4042, use Cramers rule to solve the...Ch. 3.5 - Prob. 42AP

Knowledge Booster

Background pattern image

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

Recommended textbooks for you

Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,

Text book image

Linear Algebra: A Modern Introduction

Algebra

ISBN:9781285463247

Author:David Poole

Publisher:Cengage Learning

Text book image

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:9781305658004

Author:Ron Larson

Publisher:Cengage Learning

Text book image

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:9781133382119

Author:Swokowski

Publisher:Cengage

Text book image

College Algebra

Algebra

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:Cengage Learning

Text book image

Elements Of Modern Algebra

Algebra

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Cengage Learning,

SEE MORE TEXTBOOKS

Vector Spaces | Definition & Examples; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=72GtkP6nP_A;License: Standard YouTube License, CC-BY

Understanding Vector Spaces; Author: Professor Dave Explains;https://www.youtube.com/watch?v=EP2ghkO0lSk;License: Standard YouTube License, CC-BY