Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e
5th Edition
ISBN: 9781323132098
Author: Thomas, Lay
Publisher: PEARSON C
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 3.2, Problem 2E
Each equation in Exercises 1–4 illustrates a property of determinants. State the property.
2.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Each equation in Exercises 1–4 illustrates a property of determinants. State the property.
In Exercises 17–18, evaluate each determinant.
17.
-1 -3
18.
3 4
-1 0
5|
7
4
-3
4 2
In Exercises 19–22, evaluate the (4X4) determinants.
Theorems 6–8 can be used to simplify the calculations.
Chapter 3 Solutions
Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e
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
NOTE: Write your answers using interval notation when appropriate.
CHECKING ANALYTIC SKILLS Fill in each blank ...
Graphical Approach To College Algebra
A linear equation is solved by using the intersection of graphs method. Find the solution by interpreting the g...
College Algebra with Modeling & Visualization (5th Edition)
Fill in each blank so that the resulting statement is true. An equation that expresses a relationship between t...
Algebra and Trigonometry
In Exercises 1 and 2, determine if the function f defined by the arrow diagram has an inverse. If it does, crea...
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
For the following exercises, sketch the graph, identifying the center, vertices, and foci. ( x3)264+( y2)236=1
College Algebra
True-False Review For Questions a-f, decide if the given statement is true or false, and give a brief justifica...
Differential Equations and Linear Algebra (4th 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
- In Exercises 26–34, use properties of determinants toevaluate the given determinant by inspection. Explainyour reasoning Please show all workarrow_forwardEvaluate 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-10arrow_forwardThis is a linear algebra problem. Please explain each step thoroughly.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra & 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)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
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
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
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