Linear Algebra and Its Applications (5th Edition)

5th Edition

ISBN: 9780321982384

Author: David C. Lay, Steven R. Lay, Judi J. McDonald

Publisher: PEARSON

*expand_more*

*expand_more*

*format_list_bulleted*

Textbook Question

Chapter 3.1, Problem 31E

Use Exercises 25–28 to answer the questions in Exercises 31 and 32. Give reasons for your answers.

**31.** What is the determinant of an elementary row replacement matrix?

Expert Solution & Answer

Learn your wayIncludes step-by-step video

*schedule*03:12

Students have asked these similar questions

Each equation in Exercises 1–4 illustrates a property of determinants. State the property.

In Exercises 19–22, evaluate the (4X4) determinants.
Theorems 6–8 can be used to simplify the calculations.

In Exercises 26–34, use properties of determinants toevaluate the given determinant by inspection. Explainyour reasoning
Please show all work

# Chapter 3 Solutions

Linear Algebra and Its Applications (5th Edition)

Ch. 3.1 - Compute |5722030458030506|.Ch. 3.1 - Compute the determinants in Exercises 18 using a...Ch. 3.1 - Compute the determinants in Exercises 18 using a...Ch. 3.1 - Compute the determinants in Exercises 18 using a...Ch. 3.1 - Compute the determinants in Exercises 18 using a...Ch. 3.1 - Compute the determinants in Exercises 18 using a...Ch. 3.1 - Compute the determinants in Exercises 18 using a...Ch. 3.1 - Compute the determinants in Exercises 18 using a...Ch. 3.1 - Compute the determinants in Exercises 18 using a...Ch. 3.1 - Compute the determinants in Exercises 914 by a...

Ch. 3.1 - Compute the determinants in Exercises 914 by a...Ch. 3.1 - Compute the determinants in Exercises 914 by a...Ch. 3.1 - Compute the determinants in Exercises 914 by...Ch. 3.1 - Compute the determinants in Exercises 914 by...Ch. 3.1 - Compute the determinants in Exercises 914 by...Ch. 3.1 - The expansion of a 3 3 determinant can be...Ch. 3.1 - The expansion of a 3 3 determinant can be...Ch. 3.1 - The expansion of a 3 3 determinant can be...Ch. 3.1 - The expansion of a 3 3 determinant can be...Ch. 3.1 - In Exercises 1924, explore the effect of an...Ch. 3.1 - In Exercises 1924, explore the effect of an...Ch. 3.1 - In Exercises 1924, explore the effect of an...Ch. 3.1 - In Exercises 1924, explore the effect of an...Ch. 3.1 - In Exercises 1924, explore the effect of an...Ch. 3.1 - In Exercises 1924, explore the effect of an...Ch. 3.1 - Compute the determinants of the elementary...Ch. 3.1 - Compute the determinants of the elementary...Ch. 3.1 - Compute the determinants of the elementary...Ch. 3.1 - Compute the determinants of the elementary...Ch. 3.1 - Compute the determinants of the elementary...Ch. 3.1 - Compute the determinants of the elementary...Ch. 3.1 - Use Exercises 2528 to answer the questions in...Ch. 3.1 - Use Exercises 2528 to answer the questions in...Ch. 3.1 - In Exercises 3336, verify that det EA = (det...Ch. 3.1 - In Exercises 3336, verify that det EA = (det...Ch. 3.1 - In Exercises 3336, verify that det EA = (det...Ch. 3.1 - In Exercises 3336, verify that det EA = (det...Ch. 3.1 - Let A = [3142] Write 5A. Is det 5A = 5 det A?Ch. 3.1 - Let .A = [abcd] and let k be a scalar. Find a...Ch. 3.1 - In Exercises 39 and 40, A is an n n matrix. Mark...Ch. 3.1 - a. The cofactor expansion of det A down a column...Ch. 3.1 - Let u = [30] and v = [12]. Compute the area of the...Ch. 3.1 - Let u = [ab] and v = [c0], where a, b, and c are...Ch. 3.2 - PRACTICE PROBLEMS 1. Compute |13122512045131068|...Ch. 3.2 - Use a determinant to decide if v1, v2, and v3 are...Ch. 3.2 - Let A be an n n matrix such that A2 = I. Show...Ch. 3.2 - Each equation in Exercises 14 illustrates a...Ch. 3.2 - Each equation in Exercises 14 illustrates a...Ch. 3.2 - Each equation in Exercises 14 illustrates a...Ch. 3.2 - Each equation in Exercises 14 illustrates a...Ch. 3.2 - Find the determinants in Exercises 510 by row...Ch. 3.2 - Find the determinants in Exercises 510 by row...Ch. 3.2 - Find the determinants in Exercises 510 by row...Ch. 3.2 - Find the determinants in Exercises 510 by row...Ch. 3.2 - Find the determinants in Exercises 510 by row...Ch. 3.2 - Find the determinants in Exercises 510 by row...Ch. 3.2 - Combine the methods of row reduction and cofactor...Ch. 3.2 - Combine the methods of row reduction and cofactor...Ch. 3.2 - Combine the methods of row reduction and cofactor...Ch. 3.2 - Combine the methods of row reduction and cofactor...Ch. 3.2 - Find the determinants in Exercises 1520, where 15....Ch. 3.2 - Find the determinants in Exercises 1520, where 16....Ch. 3.2 - Find the determinants in Exercises 1520, where...Ch. 3.2 - Find the determinants in Exercises 1520, where...Ch. 3.2 - Find the determinants in Exercises 1520, where...Ch. 3.2 - Find the determinants in Exercises 1520, where...Ch. 3.2 - In Exercises 2123, use determinants to find out if...Ch. 3.2 - In Exercises 2123, use determinants to find out if...Ch. 3.2 - In Exercises 2123, use determinants to find out if...Ch. 3.2 - In Exercises 2426, use determinants to decide if...Ch. 3.2 - In Exercises 2426, use determinants to decide if...Ch. 3.2 - In Exercises 2426, use determinants to decide if...Ch. 3.2 - In Exercises 27 and 28, A and B are n n matrices....Ch. 3.2 - a. If three row interchanges are made in...Ch. 3.2 - Compute det B4 where B = [101112121]Ch. 3.2 - Use Theorem 3 (but not Theorem 4) to show that if...Ch. 3.2 - Show that if A is invertible, then detA1=1detA.Ch. 3.2 - Suppose that A is a square matrix such that det A3...Ch. 3.2 - Let A and B be square matrices. Show that even...Ch. 3.2 - Let A and P be square matrices, with P invertible....Ch. 3.2 - Let U be a square matrix such that UTU = 1. Show...Ch. 3.2 - Find a formula for det(rA) when A is an n n...Ch. 3.2 - Verify that det AB = (det A)(det B) for the...Ch. 3.2 - Verify that det AB = (det A)(det B) for the...Ch. 3.2 - Let A and B be 3 3 matrices, with det A = 3 and...Ch. 3.2 - Let A and B be 4 4 matrices, with det A = 3 and...Ch. 3.2 - Prob. 41ECh. 3.2 - Let A = [1001] and B = [abcd]. Show that det(A +...Ch. 3.2 - Verify that det A = det B + det C, where A =...Ch. 3.2 - Right-multiplication by an elementary matrix E...Ch. 3.3 - Let S be the parallelogram determined by the...Ch. 3.3 - Use Cramers rule to compute the solutions of the...Ch. 3.3 - Use Cramers rule to compute the solutions of the...Ch. 3.3 - Use Cramers rule to compute the solutions of the...Ch. 3.3 - Use Cramers rule to compute the solutions of the...Ch. 3.3 - Use Cramers rule to compute the solutions of the...Ch. 3.3 - Use Cramers rule to compute the solutions of the...Ch. 3.3 - In Exercises 710, determine the values of the...Ch. 3.3 - In Exercises 710, determine the values of the...Ch. 3.3 - In Exercises 710, determine the values of the...Ch. 3.3 - In Exercises 710, determine the values of the...Ch. 3.3 - In Exercises 1116, compute the adjugate of the...Ch. 3.3 - In Exercises 1116, compute the adjugate of the...Ch. 3.3 - In Exercises 1116, compute the adjugate of the...Ch. 3.3 - In Exercises 1116, compute the adjugate of the...Ch. 3.3 - In Exercises 1116, compute the adjugate of the...Ch. 3.3 - In Exercises 1116, compute the adjugate of the...Ch. 3.3 - Show that if A is 2 2, then Theorem 8 gives the...Ch. 3.3 - Suppose that all the entries in A are integers and...Ch. 3.3 - In Exercises 1922, find the area of the...Ch. 3.3 - In Exercises 1922, find the area of the...Ch. 3.3 - In Exercises 1922, find the area of the...Ch. 3.3 - In Exercises 19-22, find the area of the...Ch. 3.3 - Find the volume of the parallelepiped with one...Ch. 3.3 - Find the volume of the parallelepiped with one...Ch. 3.3 - Use the concept of volume to explain why the...Ch. 3.3 - Let T : m n be a linear transformation, and let p...Ch. 3.3 - Let S be the parallelogram determined by the...Ch. 3.3 - Repeat Exercise 27 with b1=[47], b2=[01], and...Ch. 3.3 - Find a formula for the area of the triangle whose...Ch. 3.3 - Let R be the triangle with vertices at (x1, y1),...Ch. 3.3 - Let T: 3 3 be the linear transformation...Ch. 3.3 - Let S be the tetrahedron in 3 with vertices at the...Ch. 3 - Mark each statement True or False. Justify each...Ch. 3 - Use row operations to show that the determinants...Ch. 3 - Use row operations to show that the determinants...Ch. 3 - Prob. 4SECh. 3 - Compute the determinants in Exercises 5 and 6. 5....Ch. 3 - Compute the determinants in Exercises 5 and 6. 6....Ch. 3 - Show that the equation of the line in 2 through...Ch. 3 - Prob. 8SECh. 3 - Exercise 9 and 10 concern determinants of the...Ch. 3 - Let f(t) = det V, with x1, x2, and x3 all...Ch. 3 - Find the area of the parallelogram determined by...Ch. 3 - Use the concept of area of a parallelogram to...Ch. 3 - Prob. 13SECh. 3 - Let A,B,C,D, and I be n n matrices. Use the...Ch. 3 - Let A, B, C, and D be n n matrices with A...Ch. 3 - Let J be the n n matrix of all 1s, and consider A...Ch. 3 - Prob. 17SE

# Additional Math Textbook Solutions

Find more solutions based on key concepts

In the following exercises, use the Product Property to simplify radical expressions. 495. a. 6253 b. 1286

Intermediate Algebra

Solve each formula for the given letter . [2.3] What percent of 60 is 42? [2.4]

Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

The determinant of a matrix [abcd] is adbc (wehave seen this quantity in Exercise 2.1.13 already). Findthe dete...

Linear Algebra with Applications (2-Download)

A faucet can fill a sink in 5 minutes. It takes twice as long for the drain to empty the sink. How long will it...

Intermediate Algebra for College Students (7th Edition)

Solve each formula for the given letter . [2.3] What percent of 60 is 42? [2.4]

Elementary and Intermediate Algebra

Find a polynomial equation with real coefficients that has the given roots. –1, 4 – 2i

College Algebra (6th Edition)

Knowledge Booster

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

- Please help. This problem involves finding the matrix product. Thank you.
*arrow_forward*Compute the determinants in Exercises 1–8 using a cofactor expansion across the first row. In Exercises 1–4, also compute the determinant by a cofactor expansion down the second column.*arrow_forward*Evaluate each determinant in Exercises 1-10. 1. 5 7 2. 4 5 6 8 3 3. -4 1 4. 7 9. 6. -2 -5 5. -7 14 1 3 -4 -8 2 7. -5 8. -2 9. 10. 2 6. 2. 2. -IN-10*arrow_forward* - PLEASE ANSWER IN AN EASY-TO-READ FORMAT!!!! PLEASE AND THANK YOU!!!!
*arrow_forward*Compute the determinants in Exercises 1–8 using a cofactor expansion across the first row. In Exercises 1–4, also compute the determinant by a cofactor expansion down the second column. just number 5*arrow_forward*The vectors A = ai + bj and B = ci + dj form two sides of a parallelogram. Show that the area of the parallelogram is given by the absolute value of the following determinant. (Also see Chapter 6, Section 3.) 12.*arrow_forward*

*arrow_back_ios*

*arrow_forward_ios*

Recommended textbooks for you

- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher: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

Algebra for College Students

Algebra

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Cengage Learning

HOW TO FIND DETERMINANT OF 2X2 & 3X3 MATRICES?/MATRICES AND DETERMINANTS CLASS XII 12 CBSE; Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=bnaKGsLYJvQ;License: Standard YouTube License, CC-BY

What are Determinants? Mathematics; Author: Edmerls;https://www.youtube.com/watch?v=v4_dxD4jpgM;License: Standard YouTube License, CC-BY