Preface -- Systems Of Linear Equations And Matrices: -- Systems of linear equations -- General systems of linear equations -- Matrices -- Row transformations and equivalence of matrices -- Row-echelon form -- Homogeneous systems -- Matrix Algebra: -- Matrix arithmetic -- Inverse of a square matrix -- Properties of invertible matrices -- Matrix solutions of systems of linear equations -- Transpose of a matrix -- Graphing Calculators And Matrices: -- Matrix menu -- Inputting and editing a matrix -- Matrix arithmetic -- Calculating determinants -- Transpose of a matrix -- Solving linear systems using Gauss-Jordan elimination -- Solving linear systems using X=A-1C Special Types Of Square Matrices -- Nonsingular matrices -- Triangular, diagonal, and scalar matrices -- Involutory, idempotent, and nilpotent matrices -- Symmetric and skew-symmetric matrices -- Orthogonal matrices -- Hermitian and skew-hermitian matrices -- Determinants: -- determinant of a square matrix -- Cramer's rule -- Properties of determinant -- Vectors In R11: -- Vectors in two dimensions -- Dot product of vectors -- Vectors in R11 -- Vectors as matrices -- Vector Spaces: -- Definitions and terminology of vector spaces -- Linear independence -- Basis -- Dimension -- Row space, column space, and null space -- Rank and nullity -- Inner Product Spaces: -- Definition and terminology for inner product spaces -- Norm of a vector in an inner product space -- Cauchy-Schwarz inequality and properties of the norm -- Orthogonality in inner product spaces -- Gram-Schmidt procedure -- Linear Transformations: -- Definition and terminology for linear transformations -- Kernel and image of a linear transformation -- Matrix representation of linear transformations -- Change of basis -- Algebra of linear transformations --Linear operators on R2 and R3 -- Eigenvalues And Eigenvectors: -- Eigenvalue problem -- Useful properties of eigenvalues -- Diagonalization -- Answer key.

Book Description: An advanced Practice Makes Perfect workbook for linear algebra, designed to reinforce ideas and concepts, to provide 500 exercises and answers, to offer hundreds of solved problems--making this workbook the ideal complement to class study or self-study.

1 2