| Date
| Section
| Topics
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| Jan 11
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(1.1)
| Systems of linear equations
(a) a few words about the course
(b) matrices and applications
(c) systems of linear equations and applications
(d) matrix notation for systems of linear equations
(e) solutions of systems of linear equations:
a unique solution, infinitely many solutions or no
solution
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| Jan 13
| (1.1)
| Systems of linear equations
(a) the equivalent relation of two systems
(b) elementary row operations
(c) triangularization
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| Jan 15
| (1.1)
| Systems of linear equations
(a) backward substitution
(b) Gaussian Elimination
(c) Solving linear systems using Gaussian Elimination and
backward substitution
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Jan 18
| (1.1)
(1.2)
| Systems of linear equations
(a) more examples
Row echelon form
(b) row echelon form
(c) solutions of systems of linear equations
leading variables and free variables
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| Jan 20
| (1.2)
(1.3)
| Row echelon form
(a) reduced row echelon form
(b) Gauss-Jordan reduction
Matrix Algebra
(c) scalar multiplication
(d) matrix addition
(e) matrix multiplication
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| Jan 22
| (1.3)
| Matrix Algebra
(a) properties of matrix addition, scalar multiplication and
matrix multiplication
(b) inverse of a matrix
(c) property of inverse matrix
(d) transpose of a matrix
(e) property of transpose matrix
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Jan 25
| (1.4)
| Elementary matrices
(a) elementary matrices for 3 elementary row operations
(b) inverses of elementary matrices
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Jan 27
| (1.4)
| Matrix inversion
(a) inverse of a square matrix
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Jan 29
| (1.4)
| LU factorization
(a) elementary matrices
(b) LU factorization
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Feb 1
| (2.1)
| Determinants
(a) determinant of a square matrix
(b) compute the determinant using elementary row operations
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Feb 3
| (2.2)
| Properties of determinants
(a) properties of determinants
(b) adjoint of a matrix
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Feb 5
| (2.3)
| Cramer's Rule
(a) Cramer's Rule
(b) applications
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Feb 8
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| Review for Hour Exam 1
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Feb 10
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| Hour Exam 1
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Feb 12
| (3.1)
| Vector spaces
(a) definition
(b) vector space: Rn
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Feb 15
| (3.1)
| Vector spaces
(a) examples in Rn, Rnxm
(b) examples in Cn[a,b]
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Feb 17
| (3.2)
| Subspaces
(a) definition
(b) examples in Rn, Rnxm
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Feb 19
| (3.2)
| Subspaces
(a) more examples in Rn, Rnxm
(b) examples in Cn[a,b]
(c) the nullspace of a matrix
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Feb 22
| (3.3)
| Linear independence
(a) definition
(b) examples in Rn
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Feb 24
| (3.4)
| Basis and dimension
(a) definition of a basis of a vector space
(b) definition of the dimension of a vector space
(c) examples
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Feb 26
| (3.5)
| The row space and column space of a matrix
(a) definitions of a row space and a column space
(b) computation of row and column spaces
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Mar 1
| (3.5)
| Subspaces of a Matrix
(a) nullspace, row space and column space
(b) nullity
(c) relation of these subspaces
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Mar 3
| (4.1)
| Linear transformation
(a) definition
(b) examples
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Mar 5
| (4.1)
| Linear transformation
(a) the image of a linear transformation
(b) the kernel of a linear transformation
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Mar 8
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| Review for Hour Exam #2
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Mar 10
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| Hour Exam #2
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Mar 12
| (4.2)
| Matrix representation of linear transformations
(a) matrix representation of a linear transformation
(b) examples
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Mar 15
| (4.3)
| Change basis
(a) relation between bases
(b) change basis using the matrix of representation
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Mar 17
| (4.3)
| Change basis
(a) relation between bases
(b) change basis using the matrix of representation
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Mar 19
| (5.1)
| The scalar product in Rn
(a) definition
(b) computation
(c) applications
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Mar 22
| (5.2)
| Orthogonal subspaces
(a) definition of orthogonal
(b) orthogonal subspaces
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Mar 24
| (5.3)
| Inner product subspaces
(a) definition
(b) examples
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Mar 26
| (5.7)
| Orthogonalization
(a) the Gram-Schmidt orthogonalization process
(b) steps
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Mar 29
Apr 2
| Spring Break
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Apr 5
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| Review
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Apr 7
| (6.1)
| Eigenvalues and eigenvectors
(a) definition
(b) computation
(c) example
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Apr 9
| (6.1)
| Eigenvalues and eigenvectors
(a) more on computation
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Apr 12
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| Review for Hour Exam #3
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Apr 14
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| Hour Exam #3
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Apr 16
| (6.1)
| Eigenvalues and eigenvectors
(a) computation
(b) applications
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Apr 19
| (6.3)
| Diagonalization
definition
computation
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Apr 21
| (6.3)
| Diagonalization
(a) definition
(b) computation
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Apr 23
| (6.5)
| Quadratic forms
(a) definition
(b) computation
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Apr 26
| (6.5)
| Quadratic forms
(a) computation
(b) applications
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Apr 28
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| Review for Final
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Apr 20
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| Review for Final
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| May 1
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| Final Exam - 1:00pm - 4:00pm
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