ELEMENTARY LINEAR ALGEBRA-W/ACCESS
12th Edition
ISBN: 9781119762911
Author: Anton
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 2.2, Problem 3E
In Exercises 1–4, verify that det(A) = det(AT)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
3. Simplify the matrix expression
A(A-B) - (A+B)B-2(A - B)2 + (A + B) 2
[2 pts] 1. Let A =
[.
1 -1 0
-343
and B =
05
5 -7
304
Compute (7A - 3B) - 4(2A - B).
20
2. Let A =
= [
-2 0
1
3
]
and B =
2
3
-1 2
For each of the following, calculate the product or indicate why it is undefined:
(a) AB
(b) BA
Chapter 2 Solutions
ELEMENTARY LINEAR ALGEBRA-W/ACCESS
Ch. 2.1 - In Exercises 12, find all the minors and cofactors...Ch. 2.1 - In Exercises 12, find all the minors and cofactors...Ch. 2.1 - Let A=[41160033410144132] Find a. M13 and C13 b....Ch. 2.1 - Let A=[2311320332103214] Find a. M32 and C32 b....Ch. 2.1 - In Exercises 58, evaluate the determinant of the...Ch. 2.1 - In Exercises 58, evaluate the determinant of the...Ch. 2.1 - In Exercises 58, evaluate the determinant of the...Ch. 2.1 - In Exercises 58, evaluate the determinant of the...Ch. 2.1 - In Exercises 914, use the arrow technique of...Ch. 2.1 - In Exercises 914, use the arrow technique of...
Ch. 2.1 - In Exercises 914, use the arrow technique of...Ch. 2.1 - In Exercises 914, use the arrow technique of...Ch. 2.1 - In Exercises 914, use the arrow technique of...Ch. 2.1 - In Exercises 914, use the arrow technique of...Ch. 2.1 - In Exercises 1518, find all values of for which...Ch. 2.1 - In Exercises 1518, find all values of for which...Ch. 2.1 - In Exercises 1518, find all values of for which...Ch. 2.1 - In Exercises 1518, find all values of for which...Ch. 2.1 - Evaluate the determinant in Exercise 13 by a...Ch. 2.1 - Evaluate the determinant in Exercise 12 by a...Ch. 2.1 - In Exercises 2126, evaluate det(A) by a cofactor...Ch. 2.1 - In Exercises 2126, evaluate det(A) by a cofactor...Ch. 2.1 - In Exercises 2126, evaluate det(A) by a cofactor...Ch. 2.1 - In Exercises 2126, evaluate det(A) by a cofactor...Ch. 2.1 - In Exercises 2126, evaluate det(A) by a cofactor...Ch. 2.1 - In Exercises 2126, evaluate det(A) by a cofactor...Ch. 2.1 - In Exercises 2732, evaluate the determinant of the...Ch. 2.1 - In Exercises 2732, evaluate the determinant of the...Ch. 2.1 - In Exercises 2732, evaluate the determinant of the...Ch. 2.1 - In Exercises 2732, evaluate the determinant of the...Ch. 2.1 - In Exercises 2732, evaluate the determinant of the...Ch. 2.1 - In Exercises 2732, evaluate the determinant of the...Ch. 2.1 - In each part, show that the value of the...Ch. 2.1 - Show that the matrices A=[ab0c]andB=[de0f] commute...Ch. 2.1 - By inspection, what is the relationship between...Ch. 2.1 - Show that det(A)=12|tr(A)1tr(A2)tr(A)| for every 2...Ch. 2.1 - What can you say about an nth-order determinant...Ch. 2.1 - What is the maximum number of zeros that a 3 3...Ch. 2.1 - Explain why the determinant of a matrix with...Ch. 2.1 - prove that (x1, y1), (x2, y2), and (x3, y3) are...Ch. 2.1 - Prove that the equation of the line through the...Ch. 2.1 - Prove that if A is upper triangular and Bij is the...Ch. 2.1 - A matrix in which the entries in each row (or in...Ch. 2.1 - In parts (a)(j) determine whether the statement is...Ch. 2.1 - In parts (a)( j) determine whether the statement...Ch. 2.1 - In parts (a)(j) determine whether the statement is...Ch. 2.1 - In parts (a)(j) determine whether the statement is...Ch. 2.1 - In parts (a)(j) determine whether the statement is...Ch. 2.1 - In parts (a)(j) determine whether the statement is...Ch. 2.1 - In parts (a)( j) determine whether the statement...Ch. 2.1 - In parts (a)(j) determine whether the statement is...Ch. 2.1 - In parts (a)(j) determine whether the statement is...Ch. 2.1 - In parts (a)(j) determine whether the statement is...Ch. 2.2 - In Exercises 14, verify that det(A) = det(AT)...Ch. 2.2 - In Exercises 14, verify that det(A) = det(AT)....Ch. 2.2 - In Exercises 14, verify that det(A) = det(AT)...Ch. 2.2 - In Exercises 14, verify that det(A) = det(AT)....Ch. 2.2 - In Exercises 58, find the determinant of the given...Ch. 2.2 - In Exercises 58, find the determinant of the given...Ch. 2.2 - In Exercises 58, find the determinant of the given...Ch. 2.2 - In Exercises 58, find the determinant of the given...Ch. 2.2 - In Exercises 914, evaluate the determinant of the...Ch. 2.2 - In Exercises 914, evaluate the determinant of the...Ch. 2.2 - In Exercises 914, evaluate the determinant of the...Ch. 2.2 - In Exercises 914, evaluate the determinant of the...Ch. 2.2 - In Exercises 914, evaluate the determinant of the...Ch. 2.2 - In Exercises 914, evaluate the determinant of the...Ch. 2.2 - In Exercises 1522, evaluate the determinant, given...Ch. 2.2 - In Exercises 1522, evaluate the determinant, given...Ch. 2.2 - In Exercises 1522, evaluate the determinant, given...Ch. 2.2 - In Exercises 1522, evaluate the determinant, given...Ch. 2.2 - In Exercises 1522, evaluate the determinant, given...Ch. 2.2 - In Exercises 1522, evaluate the determinant, given...Ch. 2.2 - In Exercises 1522, evaluate the determinant, given...Ch. 2.2 - In Exercises 1522, evaluate the determinant, given...Ch. 2.2 - Use row reduction to show that...Ch. 2.2 - Verify the formulas in parts (a) and (b) and then...Ch. 2.2 - In Exercises 2528, confirm the identities without...Ch. 2.2 - In Exercises 2528, confirm the identities without...Ch. 2.2 - In Exercises 2528, confirm the identities without...Ch. 2.2 - In Exercises 2528, confirm the identities without...Ch. 2.2 - In Exercises 2930, show that det (A) = 0 without...Ch. 2.2 - In Exercises 2930, show that det (A) = 0 without...Ch. 2.2 - It can be proved that if a square matrix M is...Ch. 2.2 - It can be proved that if a square matrix M is...Ch. 2.2 - Let A be an n n matrix, and let B be the matrix...Ch. 2.2 - Find the determinant of the following matrix....Ch. 2.2 - In parts (a)(f) determine whether the statement is...Ch. 2.2 - In parts (a)(f) determine whether the statement is...Ch. 2.2 - In parts (a)(f) determine whether the statement is...Ch. 2.2 - In parts (a)(f) determine whether the statement is...Ch. 2.2 - In parts (a)(f) determine whether the statement is...Ch. 2.2 - In parts (a)(f) determine whether the statement is...Ch. 2.3 - In Exercises 14, verify that det(kA) = kn det(A)....Ch. 2.3 - In Exercises 14, verify that det(kA) = kn det(A)....Ch. 2.3 - In Exercises 14, verify that det (kA) = kn det...Ch. 2.3 - In Exercises 14, verify that det (KA) = Kn det(A)....Ch. 2.3 - In Exercises 56, verify that det (AB) = det (BA)...Ch. 2.3 - In Exercises 56, verify that det(AB) = det(BA) and...Ch. 2.3 - In Exercises 714, use determinants to decide...Ch. 2.3 - In Exercises 714, use determinants to decide...Ch. 2.3 - In Exercises 714, use determinants to decide...Ch. 2.3 - In Exercises 714, use determinants to decide...Ch. 2.3 - In Exercises 714, use determinants to decide...Ch. 2.3 - In Exercises 714, use determinants to decide...Ch. 2.3 - In Exercises 714, use determinants to decide...Ch. 2.3 - In Exercises 714, use determinants to decide...Ch. 2.3 - In Exercises 1518, find the values of k for which...Ch. 2.3 - In Exercises 1518, find the values of k for which...Ch. 2.3 - In Exercises 1518, find the values of k for which...Ch. 2.3 - In Exercises 1518, find the values of k for which...Ch. 2.3 - In Exercises 1923, decide whether the matrix is...Ch. 2.3 - In Exercises 1923, decide whether the matrix is...Ch. 2.3 - In Exercises 1923, decide whether the matrix is...Ch. 2.3 - In Exercises 1923, decide whether the matrix is...Ch. 2.3 - In Exercises 1923, decide whether the matrix is...Ch. 2.3 - In Exercises 2429, solve by Cramers rule, where it...Ch. 2.3 - In Exercises 2429, solve by Cramers rule, where it...Ch. 2.3 - In Exercises 2429, solve by Cramers rule, where it...Ch. 2.3 - In Exercises 2429, solve by Cramers rule, where it...Ch. 2.3 - In Exercises 2429, solve by Cramers rule, where it...Ch. 2.3 - In Exercises 2429, solve by Cramers rule, where it...Ch. 2.3 - Show that the matrix A=[cossin0sincos0001] is...Ch. 2.3 - Use Cramers rule to solve for the unknown y...Ch. 2.3 - Let Ax = b be the system in Exercise 31 a. Solve...Ch. 2.3 - Let A=[abcdefghi] Assuming that det(A) = 7, find...Ch. 2.3 - In each part, find the determinant given that A is...Ch. 2.3 - In each part, find the determinant given that A is...Ch. 2.3 - Prove that a square matrix A is invertible if and...Ch. 2.3 - Prove that if A is a square matrix, then det(AT) =...Ch. 2.3 - Let Ax = b be a system of n linear equations in n...Ch. 2.3 - Prove that if det(A) = 1 and all the entries in A...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - In parts (a)(l) determine whether the statement is...Ch. 2.3 - Prob. 12TFCh. 2 - In Exercises 18, evaluate the determinant of the...Ch. 2 - In Exercises 18, evaluate the determinant of the...Ch. 2 - In Exercises 18, evaluate the determinant of the...Ch. 2 - In Exercises 18, evaluate the determinant of the...Ch. 2 - In Exercises 18, evaluate the determinant of the...Ch. 2 - In Exercises 18, evaluate the determinant of the...Ch. 2 - In Exercises 18, evaluate the determinant of the...Ch. 2 - In Exercises 18, evaluate the determinant of the...Ch. 2 - Evaluate the determinants in Exercises 36 by using...Ch. 2 - a. Construct a 4 4 matrix whose determinant is...Ch. 2 - Use the determinant to decide whether the matrices...Ch. 2 - Use the determinant to decide whether the matrices...Ch. 2 - In Exercises 1315, find the given determinant by...Ch. 2 - In Exercises 1315, find the given determinant by...Ch. 2 - In Exercises 1315, find the given determinant by...Ch. 2 - Solve for x. |x131x|=|1032x613x5|Ch. 2 - In Exercises 1724, use the adjoint method (Theorem...Ch. 2 - In Exercises 1724, use the adjoint method (Theorem...Ch. 2 - In Exercises 1724, use the adjoint method (Theorem...Ch. 2 - In Exercises 1724, use the adjoint method (Theorem...Ch. 2 - In Exercises 1724, use the adjoint method (Theorem...Ch. 2 - In Exercises 1724, use the adjoint method (Theorem...Ch. 2 - In Exercises 1724, use the adjoint method (Theorem...Ch. 2 - In Exercises 1724, use the adjoint method (Theorem...Ch. 2 - Use Cramers rule to solve for x and y in terms of...Ch. 2 - Use Cramers rule to solve for x and y in terms of...Ch. 2 - By examining the determinant of the coefficient...Ch. 2 - Let A be a 3 3 matrix, each of whose entries is 1...Ch. 2 - a. For the triangle in the accompanying figure,...Ch. 2 - Use determinants to show that for all real values...Ch. 2 - Prove: If A is invertible, then adj(A) is...Ch. 2 - Prove: If A is an n n matrix, then...Ch. 2 - Prove: If the entries in each row of an n n...Ch. 2 - a. In the accompanying figure, the area of the...Ch. 2 - Use the fact that 21375, 38798, 34162, 40223,...Ch. 2 - Without directly evaluating the determinant, show...
Additional Math Textbook Solutions
Find more solutions based on key concepts
For each of the following, determine the constant c so that f(x) satisfies the conditions of being a pmf for a ...
Probability And Statistical Inference (10th Edition)
Fill in each blank so that the resulting statement is true.
1. A combination of numbers, variables, and opera...
College Algebra (7th Edition)
Checkpoint1
Use the substitution method to solve this system:
Answers to Checkpoint exercises are found at the...
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
76. Dew Point and Altitude The dew point decreases as altitude increases. If the dew point on the ground is 80°...
College Algebra with Modeling & Visualization (5th Edition)
Derivatives of bx Find the derivatives of the following functions. 24. y = 53t
Calculus: Early Transcendentals (2nd Edition)
Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis t...
Elementary Statistics: Picturing the World (7th 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
- Answer the number questions with the following answers +/- 2 sqrt(2) +/- i sqrt(6) (-3 +/-3 i sqrt(3))/4 +/-1 +/- sqrt(6) +/- 2/3 sqrt(3) 4 -3 +/- 3 i sqrt(3)arrow_forward1 Matching 10 points Factor and Solve 1)x3-216 0, x = {6,[B]} 2) 16x3 = 54 x-[3/2,[D]] 3)x4x2-42 0 x= [ +/-isqrt(7), [F] } 4)x+3-13-9x x=[+/-1.[H]] 5)x38x2+16x=0, x = {0,[K}} 6) 2x6-10x-48x2-0 x-[0, [M], +/-isqrt(3)) 7) 3x+2x²-8 x = {+/-i sqrt(2), {Q}} 8) 5x³-3x²+32x=2x+18 x = {3/5, [S]} [B] [D] [F] [H] [K] [M] [Q] +/-2 sqrt(2) +/- i sqrt(6) (-3+/-3 i sqrt(3))/4 +/- 1 +/-sqrt(6) +/- 2/3 sqrt(3) 4 -3 +/- 3 i sqrt(3) [S]arrow_forwardThe only problems I need help with ae the last 8 ones, Thanksarrow_forward
- Graph without using the calculator y-1 = | x+4 |arrow_forward9:43 AS く Akbar © Printed in the United States 15) Scale: 1 cmal unit on both axes .ill 64% The graph above shows a straight line QT intersecting the y-axis at T. i State the co-ordinates of T. ii Calculate the gradient of QT 16) iii Determine the equation of QT. A (-1, 9) ||| i L Г (5 marks)arrow_forwardPls help.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY