Solutions to Practice Problems.Īnswers to Selected Exercises.3 1 Systems of Linear Equations.ġ.1 Lines and Linear Equations.ġ.2 Linear Systems and Matrices.ġ.3 Applications of Linear Systems*.Ĥ.1 Introduction to Subspaces.ĥ.1 The Determinant Function.ĥ.2 Properties of the Determinant.ĥ.3 Applications of the Determinant*.Ħ Eigenvalues and Eigenvectors.Ħ.1 Eigenvalues and Eigenvectors.Ħ.3 Complex Eigenvalues and Eigenvectors*.Ħ.4 Systems of Differential Equations*.ħ.1 Vector Spaces and Subspaces.ħ.2 Span and Linear Independence.Ĩ.1 Dot Products and Orthogonal Sets.Ĩ.2 Projection and the Gram–Schmidt Process.Ĩ.3 Diagonalizing Symmetric Matrices and QR Factorization.Ĩ.4 The Singular Value Decomposition*.Ĩ.5 Least Squares Regression*.ĩ.1 Definition and Properties.ĩ.3 The Matrix of a Linear Transformation.ġ0.2 The Gram–Schmidt Process Revisited.ġ0.3 Applications of Inner Products*.ġ1 Additional Topics and Applications*.ġ1.2 Positive Definite Matrices.ġ1.3 Constrained Optimization.
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