Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
Author: Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
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Textbook Question
Chapter 3.1, Problem 12P
For Problems 12—15, determine the values of the indices p and q such that the following are terms in a determinant of order 4. In each case, determine the number of inversions in the permutation of the column indices and hence find the appropriate sign that should attached to each term.
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Question 1. Solve the system
-
x1 x2 + 3x3 + 2x4
-x1 + x22x3 + x4
2x12x2+7x3+7x4
Question 2. Consider the system
= 1
=-2
= 1
3x1 - x2 + ax3
= 1
x1 + 3x2 + 2x3
x12x2+2x3
= -b
= 4
1 For what values of a, b will the system be inconsistent?
2 For what values of a, b will the system have only one solution?
For what values of a, b will the saystem have infinitely many solutions?
Chapter 3 Solutions
Differential Equations and Linear Algebra (4th Edition)
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. 5PCh. 3.1 - Prob. 6PCh. 3.1 - Use Definition 3.1.8 to derive the general...
Ch. 3.1 - Prob. 11PCh. 3.1 - For Problems 1215, determine the values of the...Ch. 3.1 - Prob. 13PCh. 3.1 - Prob. 14PCh. 3.1 - For Problems 1215, determine the values of the...Ch. 3.1 - Prob. 16PCh. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 18PCh. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 20PCh. 3.1 - Prob. 21PCh. 3.1 - Prob. 22PCh. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 24PCh. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 26PCh. 3.1 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - Prob. 29PCh. 3.1 - Prob. 30PCh. 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. 36PCh. 3.1 - Prob. 37PCh. 3.1 - Prob. 38PCh. 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. 42PCh. 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. 45PCh. 3.1 - Prob. 46PCh. 3.1 - In Problem 4748, we explore a relationship between...Ch. 3.1 - Prob. 48PCh. 3.1 - (a) Write all 24 distinct permutations of the...Ch. 3.1 - Prob. 50PCh. 3.1 - Prob. 52PCh. 3.1 - 3.1Problems a) If A=[a11a12a21a22] and c is a...Ch. 3.1 - Prob. 55PCh. 3.1 - Prob. 56PCh. 3.1 - Let A be an arbitrary 44 matrix. By experimenting...Ch. 3.1 - Prob. 59PCh. 3.2 - For items a-f, decide if the given statement is...Ch. 3.2 - Prob. 2TFRCh. 3.2 - For items a-f, decide if the given statement is...Ch. 3.2 - Prob. 4TFRCh. 3.2 - Prob. 5TFRCh. 3.2 - Prob. 6TFRCh. 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. 8PCh. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 10PCh. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 12PCh. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 14PCh. 3.2 - For Problems 1521, use Theorem 3.2.5 to determine...Ch. 3.2 - Prob. 16PCh. 3.2 - For Problems 1521, use Theorem 3.2.5 to determine...Ch. 3.2 - Prob. 18PCh. 3.2 - Prob. 19PCh. 3.2 - Prob. 20PCh. 3.2 - For Problems 1521, use Theorem 3.2.5 to determine...Ch. 3.2 - Prob. 22PCh. 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. 27PCh. 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. 31PCh. 3.2 - Prob. 32PCh. 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. 36PCh. 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. 49PCh. 3.2 - Prob. 50PCh. 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. 55PCh. 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. 60PCh. 3.2 - Let A be general 44 matrix. a Verify property P1...Ch. 3.2 - Prob. 62PCh. 3.2 - Determine all values of a for which...Ch. 3.2 - Prob. 64PCh. 3.2 - Prob. 65PCh. 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. 5TFRCh. 3.3 - Prob. 6TFRCh. 3.3 - Prob. 7TFRCh. 3.3 - Prob. 8TFRCh. 3.3 - Prob. 9TFRCh. 3.3 - Prob. 1PCh. 3.3 - Prob. 2PCh. 3.3 - For Problems 1-4, determine all minors and...Ch. 3.3 - Prob. 4PCh. 3.3 - Prob. 5PCh. 3.3 - Prob. 6PCh. 3.3 - Prob. 7PCh. 3.3 - Prob. 8PCh. 3.3 - For Problems 7-14, use the cofactor expansion...Ch. 3.3 - Prob. 10PCh. 3.3 - Prob. 11PCh. 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. 14PCh. 3.3 - For Problems 1522, evaluate the given determinant...Ch. 3.3 - Prob. 16PCh. 3.3 - Prob. 17PCh. 3.3 - Prob. 18PCh. 3.3 - Prob. 19PCh. 3.3 - For Problems 1522, evaluate the given determinant...Ch. 3.3 - For Problems 1522, evaluate the given determinant...Ch. 3.3 - Prob. 22PCh. 3.3 - Prob. 23PCh. 3.3 - Prob. 24PCh. 3.3 - Prob. 25PCh. 3.3 - Prob. 26PCh. 3.3 - Prob. 27PCh. 3.3 - Prob. 28PCh. 3.3 - Prob. 29PCh. 3.3 - Prob. 30PCh. 3.3 - Prob. 31PCh. 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. 37PCh. 3.3 - Prob. 39PCh. 3.3 - Prob. 40PCh. 3.3 - Prob. 41PCh. 3.3 - Prob. 42PCh. 3.3 - Prob. 43PCh. 3.3 - Prob. 44PCh. 3.3 - Prob. 45PCh. 3.3 - Prob. 46PCh. 3.3 - Prob. 47PCh. 3.3 - Prob. 48PCh. 3.3 - Prob. 49PCh. 3.3 - Prob. 50PCh. 3.3 - Prob. 51PCh. 3.3 - Prob. 52PCh. 3.3 - Prob. 53PCh. 3.3 - Prob. 54PCh. 3.3 - Prob. 55PCh. 3.3 - Prob. 57PCh. 3.3 - Prob. 58PCh. 3.3 - Prob. 59PCh. 3.3 - Prob. 60PCh. 3.3 - For Problems 59-64, use Cramers rule to solve the...Ch. 3.3 - Prob. 62PCh. 3.3 - Prob. 63PCh. 3.3 - Prob. 64PCh. 3.3 - Prob. 65PCh. 3.3 - Prob. 66PCh. 3.3 - Prob. 67PCh. 3.3 - Prob. 68PCh. 3.3 - Prob. 69PCh. 3.3 - Let A be a randomly generated invertible 44...Ch. 3.3 - Prob. 72PCh. 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. 6PCh. 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. 9PCh. 3.4 - Prob. 10PCh. 3.4 - Prob. 11PCh. 3.4 - For problems 9-14, find det(A). If A is...Ch. 3.4 - Prob. 13PCh. 3.4 - For problems 9-14, find det(A). If A is...Ch. 3.4 - Prob. 15PCh. 3.4 - Prob. 16PCh. 3.4 - For Problems 15-20, use Cramers rule to determine...Ch. 3.4 - Prob. 18PCh. 3.4 - For Problems 15-20, use Cramers rule to determine...Ch. 3.4 - Prob. 20PCh. 3.4 - Prob. 21PCh. 3.4 - Prob. 22PCh. 3.4 - Prob. 23PCh. 3.4 - For Problems 23-29, assume that A and B be 33...Ch. 3.4 - Prob. 25PCh. 3.4 - Prob. 26PCh. 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. 29PCh. 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. 6APCh. 3.5 - Prob. 7APCh. 3.5 - Prob. 8APCh. 3.5 - Prob. 9APCh. 3.5 - Prob. 10APCh. 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. 13APCh. 3.5 - Prob. 14APCh. 3.5 - Prob. 15APCh. 3.5 - Prob. 16APCh. 3.5 - Prob. 17APCh. 3.5 - Prob. 18APCh. 3.5 - Prob. 19APCh. 3.5 - Prob. 20APCh. 3.5 - Prob. 21APCh. 3.5 - Prob. 22APCh. 3.5 - Prob. 23APCh. 3.5 - Prob. 24APCh. 3.5 - Prob. 25APCh. 3.5 - Prob. 26APCh. 3.5 - Prob. 27APCh. 3.5 - Prob. 28APCh. 3.5 - Prob. 29APCh. 3.5 - Prob. 30APCh. 3.5 - Prob. 31APCh. 3.5 - Prob. 32APCh. 3.5 - Prob. 33APCh. 3.5 - True or false: Given any real number r and any 33...Ch. 3.5 - Prob. 35APCh. 3.5 - Prob. 36APCh. 3.5 - Prob. 37APCh. 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
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