Student Solution Manual for Linear Algebra

by Fraleigh, John B.

• ISBN13: 9780201526776
• ISBN10: 0201526778
• Edition: 3rd
• Format: Paperback
• Copyright: 1995-01-31
• Publisher: Pearson

Summary

Fraleigh and Beauregard's text is known for its clear presentation and writing style, mathematical appropriateness, and overall usability. Its inclusion of calculus-related examples, true/false problems, section summaries, integrated applications, and coverage of Cn make it a superb text for the sophomore or junior-level linear algebra course. This Third Edition retains the features that have made it successful over the years, while addressing recent developments of how linear algebra is taught and learned. Key concepts are presented early on, with an emphasis on geometry. KEY TOPICS: Vectors, Matrices, and Linear Systems; Dimension, Rank, and Linear Transformations; Vector Spaces; Determinants; Eigenvalues and Eigenvectors; Orthogonality; Change of Basis; Eigenvalues: Further Applications and Computations; Complex Scalars; Solving Large Linear Systems MARKET: For all readers interested in linear algebra.

Table of Contents

Vectors, Matrices, and Linear Systems	1	(21)
Vectors in Euclidean Spaces	1	(2)
The Norm and the Dot Product	3	(2)
Matrices and Their Algebra	5	(2)
Solving Systems of Linear Equations	7	(4)
Inverses of Square Matrices	11	(3)
Homogeneous Systems, Subspaces, and Bases	14	(3)
Application to Population Distribution (Optional)	17	(2)
Application to Binary Linear Codes (Optional)	19	(2)
Independence and Linear Transformations of Rn	21	(9)
Independence and Dimension	21	(1)
The Rank of a Matrix	22	(1)
Linear Transformations of Euclidean Spaces	23	(2)
Linear Transformations of the Plane (Optional)	25	(2)
Lines and Other Translates (Optional)	27	(3)
Vector Spaces	30	(15)
Vector Spaces	30	(2)
Basic Concepts of Vector Spaces	32	(4)
Coordinatization of Vectors	36	(2)
Linear Transformations	38	(5)
Inner-Product Spaces (Optional)	43	(2)
Determinants	45	(13)
Areas, Volumes, and Cross Products	45	(3)
The Determinant of a Square Matrix	48	(2)
Computation of Determinants and Cramer's Rule	50	(4)
Linear Transformations and Determinants (Optional)	54	(4)
Eigenvalues and Eigenvectors	58	(16)
Eigenvalues and Eigenvectors	58	(7)
Diagonalization	65	(4)
Two Applications	69	(5)
Orthogonality	74	(16)
Projections	74	(2)
The Gram-Schmidt Process	76	(3)
Orthogonal Matrices	79	(4)
The Projection Matrix	83	(3)
The Method of Least Squares	86	(4)
Change of Basis	90	(7)
Coordinatization and Change of Basis	90	(2)
Matrix Representations and Similarity	92	(5)
Eigenvalues: Further Applications and Computations	97	(14)
Diagonalization of Quadratic Forms	97	(3)
Applications to Geometry	100	(4)
Applications to Extrema	104	(4)
Computing Eigenvalues and Eigenvectors	108	(3)
Complex Scalars	111	(17)
Algebra of Complex Numbers	111	(2)
Matrices and Vector Spaces with Complex Scalars	113	(5)
Eigenvalues and Diagonalization	118	(4)
Jordan Canonical Form	122	(6)
Solving Large Linear Systems	128	(9)
Considerations of Time	128	(3)
The LU-Factorization	131	(4)
Pivoting, Scaling, and Ill-conditioned Matrices	135	(2)
Appendix A Mathematical Induction	137