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Math Algebra Differential Equations and Linear Algebra (4th Edition)

Let A be a randomly generated invertible 4 × 4 matrix. Verify cofactor expansion theorem for expansion along row 1.

Let A be a randomly generated invertible 4 × 4 matrix. Verify cofactor expansion theorem for expansion along row 1.

Solution Summary: The author explains the determinant of randomly generated invertible A using cofactor expansion theorem.

Differential Equations and Linear Algebra (4th Edition)

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 3.3, Problem 70P

Let A be a randomly generated invertible 4 × 4 matrix. Verify cofactor expansion theorem for expansion along row 1.

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Chapter 3.3, Problem 69P

Chapter 3.3, Problem 72P

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. 5P Ch. 3.1 - Prob. 6P Ch. 3.1 - Use Definition 3.1.8 to derive the general...

Ch. 3.1 - Prob. 11P Ch. 3.1 - For Problems 1215, determine the values of the...Ch. 3.1 - Prob. 13P Ch. 3.1 - Prob. 14P Ch. 3.1 - For Problems 1215, determine the values of the...Ch. 3.1 - Prob. 16P Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 18P Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 20P Ch. 3.1 - Prob. 21P Ch. 3.1 - Prob. 22P Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 24P Ch. 3.1 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 26P Ch. 3.1 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - Prob. 29P Ch. 3.1 - Prob. 30P 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 - For Problem 1642 evaluate the determinant of...Ch. 3.1 - Prob. 36P Ch. 3.1 - Prob. 37P Ch. 3.1 - Prob. 38P 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 - For Problems 16-42, evaluate the determinant of...Ch. 3.1 - Prob. 42P Ch. 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. 45P Ch. 3.1 - Prob. 46P Ch. 3.1 - In Problem 4748, we explore a relationship between...Ch. 3.1 - Prob. 48P Ch. 3.1 - (a) Write all 24 distinct permutations of the...Ch. 3.1 - Prob. 50P Ch. 3.1 - Prob. 52P Ch. 3.1 - 3.1Problems a) If A=[a11a12a21a22] and c is a...Ch. 3.1 - Prob. 55P Ch. 3.1 - Prob. 56P Ch. 3.1 - Let A be an arbitrary 44 matrix. By experimenting...Ch. 3.1 - Prob. 59P Ch. 3.2 - For items a-f, decide if the given statement is...Ch. 3.2 - Prob. 2TFR Ch. 3.2 - For items a-f, decide if the given statement is...Ch. 3.2 - Prob. 4TFR Ch. 3.2 - Prob. 5TFR Ch. 3.2 - Prob. 6TFR 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 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 8P Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 10P Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 12P Ch. 3.2 - For Problems 1-14, evaluate the determinant of the...Ch. 3.2 - Prob. 14P Ch. 3.2 - For Problems 1521, use Theorem 3.2.5 to determine...Ch. 3.2 - Prob. 16P Ch. 3.2 - For Problems 1521, use Theorem 3.2.5 to determine...Ch. 3.2 - Prob. 18P Ch. 3.2 - Prob. 19P Ch. 3.2 - Prob. 20P Ch. 3.2 - For Problems 1521, use Theorem 3.2.5 to determine...Ch. 3.2 - Prob. 22P 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 - 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. 27P Ch. 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. 31P Ch. 3.2 - Prob. 32P 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 - For Problems 33-36, let A=[abcdefghi] and assume...Ch. 3.2 - Prob. 36P 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 - 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. 49P Ch. 3.2 - Prob. 50P Ch. 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. 55P Ch. 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. 60P Ch. 3.2 - Let A be general 44 matrix. a Verify property P1...Ch. 3.2 - Prob. 62P Ch. 3.2 - Determine all values of a for which...Ch. 3.2 - Prob. 64P Ch. 3.2 - Prob. 65P Ch. 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. 5TFR Ch. 3.3 - Prob. 6TFR Ch. 3.3 - Prob. 7TFR Ch. 3.3 - Prob. 8TFR Ch. 3.3 - Prob. 9TFR Ch. 3.3 - Prob. 1P Ch. 3.3 - Prob. 2P Ch. 3.3 - For Problems 1-4, determine all minors and...Ch. 3.3 - Prob. 4P Ch. 3.3 - Prob. 5P Ch. 3.3 - Prob. 6P Ch. 3.3 - Prob. 7P Ch. 3.3 - Prob. 8P Ch. 3.3 - For Problems 7-14, use the cofactor expansion...Ch. 3.3 - Prob. 10P Ch. 3.3 - Prob. 11P Ch. 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. 14P Ch. 3.3 - For Problems 1522, evaluate the given determinant...Ch. 3.3 - Prob. 16P Ch. 3.3 - Prob. 17P Ch. 3.3 - Prob. 18P Ch. 3.3 - Prob. 19P Ch. 3.3 - For Problems 1522, evaluate the given determinant...Ch. 3.3 - For Problems 1522, evaluate the given determinant...Ch. 3.3 - Prob. 22P Ch. 3.3 - Prob. 23P Ch. 3.3 - Prob. 24P Ch. 3.3 - Prob. 25P Ch. 3.3 - Prob. 26P Ch. 3.3 - Prob. 27P Ch. 3.3 - Prob. 28P Ch. 3.3 - Prob. 29P Ch. 3.3 - Prob. 30P Ch. 3.3 - Prob. 31P 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 - For Problems 3138, determine the eigenvalues of...Ch. 3.3 - Prob. 37P Ch. 3.3 - Prob. 39P Ch. 3.3 - Prob. 40P Ch. 3.3 - Prob. 41P Ch. 3.3 - Prob. 42P Ch. 3.3 - Prob. 43P Ch. 3.3 - Prob. 44P Ch. 3.3 - Prob. 45P Ch. 3.3 - Prob. 46P Ch. 3.3 - Prob. 47P Ch. 3.3 - Prob. 48P Ch. 3.3 - Prob. 49P Ch. 3.3 - Prob. 50P Ch. 3.3 - Prob. 51P Ch. 3.3 - Prob. 52P Ch. 3.3 - Prob. 53P Ch. 3.3 - Prob. 54P Ch. 3.3 - Prob. 55P Ch. 3.3 - Prob. 57P Ch. 3.3 - Prob. 58P Ch. 3.3 - Prob. 59P Ch. 3.3 - Prob. 60P Ch. 3.3 - For Problems 59-64, use Cramers rule to solve the...Ch. 3.3 - Prob. 62P Ch. 3.3 - Prob. 63P Ch. 3.3 - Prob. 64P Ch. 3.3 - Prob. 65P Ch. 3.3 - Prob. 66P Ch. 3.3 - Prob. 67P Ch. 3.3 - Prob. 68P Ch. 3.3 - Prob. 69P Ch. 3.3 - Let A be a randomly generated invertible 44...Ch. 3.3 - Prob. 72P Ch. 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. 6P 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. 9P Ch. 3.4 - Prob. 10P Ch. 3.4 - Prob. 11P Ch. 3.4 - For problems 9-14, find det(A). If A is...Ch. 3.4 - Prob. 13P Ch. 3.4 - For problems 9-14, find det(A). If A is...Ch. 3.4 - Prob. 15P Ch. 3.4 - Prob. 16P Ch. 3.4 - For Problems 15-20, use Cramers rule to determine...Ch. 3.4 - Prob. 18P Ch. 3.4 - For Problems 15-20, use Cramers rule to determine...Ch. 3.4 - Prob. 20P Ch. 3.4 - Prob. 21P Ch. 3.4 - Prob. 22P Ch. 3.4 - Prob. 23P Ch. 3.4 - For Problems 23-29, assume that A and B be 33...Ch. 3.4 - Prob. 25P Ch. 3.4 - Prob. 26P Ch. 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. 29P 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 1-6, evaluate the determinant of the...Ch. 3.5 - For Problems 16, evaluate the determinant of the...Ch. 3.5 - Prob. 6AP Ch. 3.5 - Prob. 7AP Ch. 3.5 - Prob. 8AP Ch. 3.5 - Prob. 9AP Ch. 3.5 - Prob. 10AP Ch. 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. 13AP Ch. 3.5 - Prob. 14AP Ch. 3.5 - Prob. 15AP Ch. 3.5 - Prob. 16AP Ch. 3.5 - Prob. 17AP Ch. 3.5 - Prob. 18AP Ch. 3.5 - Prob. 19AP Ch. 3.5 - Prob. 20AP Ch. 3.5 - Prob. 21AP Ch. 3.5 - Prob. 22AP Ch. 3.5 - Prob. 23AP Ch. 3.5 - Prob. 24AP Ch. 3.5 - Prob. 25AP Ch. 3.5 - Prob. 26AP Ch. 3.5 - Prob. 27AP Ch. 3.5 - Prob. 28AP Ch. 3.5 - Prob. 29AP Ch. 3.5 - Prob. 30AP Ch. 3.5 - Prob. 31AP Ch. 3.5 - Prob. 32AP Ch. 3.5 - Prob. 33AP Ch. 3.5 - True or false: Given any real number r and any 33...Ch. 3.5 - Prob. 35AP Ch. 3.5 - Prob. 36AP Ch. 3.5 - Prob. 37AP Ch. 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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