Math 2568 - Autumn 2020

• Lecture 1 (§ 1.1: Introduction to Matrices And Systems of Linear Equations), August 26, 2020. [Slides]
• Lecture 2 (§ 1.1 (cont.): Introduction to Matrices And Systems of Linear Equations, and § 1.2: Echelon Form and Gauss-Jordan Elimination), August 28, 2020. [Slides pre-class], [Slides post class]
• Lecture 3 (§ 1.2 (cont.): Echelon Form and Gauss-Jordan Elimination), August 31, 2020.
  [Slides pre-class], [Slides post class]
• Lecture 4 (§ 1.3: Consistent Systems of Linear Equations), September 2, 2020.
  [Slides pre-class], [Slides post class]
• Lecture 5 (§ 1.3 (cont.): Homogeneous Systems, and interpolation of points via curves in the plane), September 4, 2020. [Slides pre-class], [Slides post class]. [Drawing Conics using Wolframalpha]
• Lecture 6 (§ 1.5 Matrix operations), September 9, 2020. [Slides pre-class], [Slides post class]
• Lecture 7 (§ 1.6: Algebraic Properties of Matrix Operations), September 11, 2020. [Slides pre-class], [Slides post class]
• Lecture 8 (§ 1.9: Matrix Inverses and Their Properties), September 14, 2020. [Slides pre-class], [Slides post class]
• Lecture 9 (§ 1.7: Linear independence and Nonsingular Matrices), September 16, 2020. [Slides pre-class], [Slides post class]
• Lecture 10 (§ 2.1: Vectors in the Plane, and § 2.2: Vectors in Space), September 18, 2020. [Slides pre-class], [Slides post class]
• Lecture 11 (§ 2.3: The Dot Product and the Cross Product), September 23, 2020. [Slides pre-class], [Slides post class]
• Lecture 12 (§ 2.3 (cont.): The Cross Product, and § 2.4: Lines in the Plane and in Space), September 25, 2020. [Slides pre-class], [Slides post class]
• Lecture 13 (§ 2.4 (cont.): Planes in Space), September 28, 2020. [Slides pre-class], [Slides post class]
• Lecture 14 (§ 3.1: Introduction to the Vector Space Rⁿ, and § 3.2: Vector Space Properties of Rⁿ), September 30, 2020. [Slides pre-class], [Slides post class]
• Lecture 15 (§ 3.3: More Examples of Subspaces), October 2, 2020. [Slides pre-class], [Slides post class]
• Lecture 16 (§ 3.4: Bases for Subspaces), October 5, 2020. [Slides pre-class], [Slides post class]
• Lecture 17 (§ 3.4 (cont.): Bases for Subspaces, and § 3.5: Dimension of subspaces of Rⁿ), October 7, 2020. [Slides pre-class], [Slides post class]
• Lecture 18 (§ 3.6: Orthogonal Bases for Subspaces), October 9, 2020. [Slides pre-class], [Slides post class]
• Lecture 19 (§ 3.7: Linear Transformation from Rⁿ to R^m), October 12, 2020. [Slides pre-class], [Slides post class]
• Lecture 20 (§ 3.7 (cont.): Linear Transformation from Rⁿ to R^m ), October 14, 2020. [Slides pre-class], [Slides post class]
• Lecture 21 (§ 5.1: Introduction to Vector Spaces and Linear Transformations, and § 5.2: Vector Spaces), October 16, 2020. [Slides pre-class], [Slides post class]
• Lecture 22 (§ 5.3: Subspaces), October 21, 2020. [Slides pre-class], [Slides post class]
• Lecture 23 (§ 5.4: Linear Independence and Bases), october 23, 2020. [Slides pre-class], [Slides post class]
• Lecture 24 (§ 5.4 (cont.): Linear Independence and Bases), October 26, 2020. [Slides pre-class], [Slides post class]
• Lecture 25 (§ 5.7: Linear Transformations: Null space and range, the Rank-Nullity Theorem), October 28, 2020. [Slides pre-class], [Slides post class]
• Lecture 26 (§ 5.8: Operations With Linear Transformations: addition, scalar multiplication, composition; surjective and invertible transformations; examples), October 30, 2020. [Slides pre-class], [Slides post class]
• Lecture 27 (§ 5.9: Matrix Representations Of Linear Transformations), November 2, 2020. [Slides pre-class], [Slides post class]
• Lecture 28 (§ 6.1: Introduction to Determinants and § 6.2: Cofactor Expansions Of Determinants), November 4, 2020. [Slides pre-class], [Slides post class]
• Lecture 29 (§ 6.3: Elementary Operations And Determinants), November 6, 2020. [Slides pre-class], [Slides post class]
• Lecture 30 (§ 6.4: Cramer's Rule [Slides pre-class], [Slides post class] ), November 9, 2020.
• Lecture 31 (§ 4.1: The Eigenvalue Problem for (2 × 2) Matrices, and § 4.2: Determinants and the Eigenvalue Problem), November 13, 2020. [Slides pre-class], [Slides post class]
• Lecture 32 (§ 4.4: Eigenvalues and the Characteristic Polynomial), November 18, 2020. [Slides pre-class], [Slides post class]
• Lecture 33 (§ 4.5: Eigenvectors and Eigenspaces; Defective matrices), November 20, 2020. [Slides pre-class], [Slides post class]
• Lecture 34 (§ 4.6: Complex numbers and complex eigenvalues; roots of non-constant polynomials with real coefficients), November 23, 2020. [Slides pre-class], [Slides post class]
• Lecture 35 (§ 4.6: Complex Eigenvectors and Eigenspaces; real symmetric matrices), November 25, 2020. [Slides pre-class], [Slides post class]
• Lecture 36 (§ 4.7: Similarity Transformations and Diagonalization), November 30, 2020. [Slides pre-class], [Slides post class]
• Lecture 37 (§ 4.7 (cont.): Similarity Transformations and Diagonalization), December 2, 2020. [Slides pre-class], [Slides post class]

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