Linear AlgebraChapter 1 Linear Equations in Linear Algebra 1-1 Systems of Linear Equations 1-2 Row Reduction and Echelon Forms1-3 Vector Equations 1-4 The Matrix Equation Ax = b 1-5 Solution Sets of Linear Systems1-6 Applications of Linear Systems1-7 Linear Independence 1-8 Introduction to Linear Transformations1-9 The Matrix of a Linear Transformation Chapter 2 Matrix Algebra 2-1 Matrix Operations 2-2 The Inverse of a Matrix 2-3 Characterizations of Invertible Matrices2-4 Partitioned Matrices 2-5 Matrix Factorizations 2-6 The Leontief Input-Output Model 2-7 Applications to Computer Graphics Chapter 3 Determinants 3-1 Introduction to Determinants 1723-2 Properties of Determinants 1793-3 Cramer's Rule, Volume, and Linear Transformations Chapter 4 Vector Spaces 4-1 Vector Spaces and Subspaces4-2 Null Spaces, Column Spaces, Row Spaces, and Linear Transformations 4-3 Linearly Independent Sets; Bases4-4 Coordinate Systems4-5 The Dimension of a vector space4-6 Change of Basis4-7 Digital Signal Processing4-8 Applications to Difference Equations Chapter 5 Eigenvalues and Eigenvectors 5-1 Eigenvalues and Eigenvectors5-2 The Characteristic Equation5-3 Diaganolization5-4 Eigenvectors. And Linear Transformation5-5 Complex Eigenvalues5-6 Discrete Dynamical Systems Chapter 6 Orthogonality and Least Squares 6.1 Inner Product, Length, and Orthogonality6.2 Orthogonal Sets 6.3 Orthogonal Projections 6.4 The Gram-Schmidt Process 6.5 Least-Squares Problems 6.7 Inner Product Spaces 6.8 Applications of Inner product Spaces Chapter 7 Symmetric Matrices and Quadratic Forms 7.1 Diagonalization of Symmetric Matrices7.2 Quadratic Forms7.3 Constrained Optimization7.4 The Singular Value Decomposition7.5 Applications to Image Processing and Statistics Find an SVD for [-3 1]

Question

Linear AlgebraChapter 1 Linear Equations in Linear Algebra 1-1 Systems of Linear Equations 1-2 Row Reduction and Echelon Forms1-3 Vector Equations 1-4 The Matrix Equation Ax = b 1-5 Solution Sets of Linear Systems1-6 Applications of Linear Systems1-7 Linear Independence 1-8 Introduction to Linear Transformations1-9 The Matrix of a Linear Transformation  Chapter 2 Matrix Algebra 2-1 Matrix Operations 2-2 The Inverse of a Matrix 2-3 Characterizations of Invertible Matrices2-4 Partitioned Matrices 2-5 Matrix Factorizations 2-6 The Leontief Input-Output Model 2-7 Applications to Computer Graphics Chapter 3 Determinants 3-1 Introduction to Determinants 1723-2 Properties of Determinants 1793-3 Cramer's Rule, Volume, and Linear Transformations Chapter 4 Vector Spaces 4-1 Vector Spaces and Subspaces4-2 Null Spaces, Column Spaces, Row Spaces, and Linear Transformations 4-3 Linearly Independent Sets; Bases4-4 Coordinate Systems4-5 The Dimension of a vector space4-6 Change of Basis4-7 Digital Signal Processing4-8 Applications to Difference Equations Chapter 5 Eigenvalues and Eigenvectors 5-1 Eigenvalues and Eigenvectors5-2 The Characteristic Equation5-3 Diaganolization5-4 Eigenvectors. And Linear Transformation5-5 Complex Eigenvalues5-6 Discrete Dynamical Systems Chapter 6 Orthogonality and Least Squares 6.1 Inner Product, Length, and Orthogonality6.2 Orthogonal Sets 6.3 Orthogonal Projections 6.4 The Gram-Schmidt Process 6.5 Least-Squares Problems 6.7 Inner Product Spaces 6.8 Applications of Inner product Spaces Chapter 7 Symmetric Matrices and Quadratic Forms 7.1 Diagonalization of Symmetric Matrices7.2 Quadratic Forms7.3 Constrained Optimization7.4 The Singular Value Decomposition7.5 Applications to Image Processing and Statistics Find an SVD for [-3 1]

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