This problem manual exploits the power of DERIVE software in order to help students learn linear algebra concepts. Each chapter begins with worked examples, which include DERIVE instructions, followed by realistic exercises and substantial exploration and discovery problems which encourage students to explore ideas on their own.
Systems of Equations; Augmented Matrices and Elementary Row Operations; The Algebra of Matrices; Invernesses of Matrices; Determinants, Adjoints and Cramers Rule; Matrix Algebra and Modular Arithmetic; Vector Products, Lines and Planes; Vector Spaces and Subspaces; Independence, Basis and Dimension; Row Space, Column Space and Null Space; Inner Product Spaces; Orthonormal Bases and the Gram-Schmidt Process; Change of Basis and Orthogonal Matrices; Eigenvalues and Eigenvectors; Diagonalization and Orthogonal Diagonalization; Matrices and Linear Transformations from RN to RM; Matrices of General Linear Transformation Similarity; Applications and Numerical Methods.