Elementary Linear Algebra: Applications Version
Elementary Linear Algebra: Applications Version
12th Edition
ISBN: 9781119282365
Author: Howard Anton, Chris Rorres, Anton Kaul
Publisher: WILEY
bartleby

Concept explainers

Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
bartleby

Videos

Textbook Question
Book Icon
Chapter 2.3, Problem 31E

Use Cramer’s rule to solve for the unknown y without solving for the unknowns x, z, and w.

4 x +    y +   z +    w =     6 3 x + 7 y −   z +    w =     1 7 x + 3 y − 5 z + 8 w = − 3     x +   y +    z + 2 w =    3

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 2.3, Problem 30E
Next
Chapter 2.3, Problem 32E

Chapter 2 Solutions

Elementary Linear Algebra: Applications Version

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 a population containing N=902 individual, what code number would you assign for a. the first person on the ...

Basic Business Statistics, Student Value Edition

Fill in each blank so that the resulting statement is true. 1. A combination of numbers, variables, and opera...

College Algebra (7th Edition)

The table by using the given graph of h.

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Cylinder and paraboloids Find the volume of the region bounded below by the paraboloid z = x2 + y2, laterally b...

University Calculus: Early Transcendentals (4th Edition)

In Problems 51-66, find the domain of each function. g( x )= x x 2 -16

Precalculus

3. For the same sample statistics, which level of confidence would produce the widest confidence interval? Expl...

Elementary Statistics: Picturing the World (7th Edition)

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
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
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: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
SEE MORE TEXTBOOKS
What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY