Workbook 22

Chapter 1: Span

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Objectives

Be able to determine the span of vectors in either a line, a plane, or all numbers

Prerequisites

Understand linear combinations of vectors. from Chapter 3: "Linear Combinations of Vectors" in Workbook 21
lin_independence (Missing reference)
Be able to identify and understand the fundamental subspaces: nullspace, rowspace, and columnspace. from Chapter 6: "Subspaces" in Workbook 21

Chapter 2: Determinants and Inverse Matrices

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Objectives

Be able to find the determinant and understand what different values of it mean

Video: The determinant | Chapter 6, Essence of linear algebra - YouTube
Video: Determinant of 3x3 Matrices, 2x2 Matrix, Precalculus Video Tutorial - YouTube
Video: 3 x 3 determinant | Matrix transformations | Linear Algebra | Khan Academy - YouTube
Video: Interpreting determinants in terms of area | Matrices | Precalculus | Khan Academy - YouTube
Video: Finding the determinant of a 2x2 matrix | Matrices | Precalculus | Khan Academy - YouTube
Video: 18. Properties of Determinants - YouTube
Video: Properties of Determinants - YouTube
Video: Determinants | MIT 18.02SC Multivariable Calculus, Fall 2010 - YouTube
Reference: Determinant - Wikipedia
Reference: Leibniz formula for determinants - Wikipedia
Reference: Laplace expansion - Wikipedia
Reference: 3Blue1Brown - The determinant

Be able to to find inverses of matrices, and use them for practical vector problems.

Prerequisites

Transform systems of equations into matrices. Understand Gaussian and Gauss-Jordan Elimination, Row Echelon Form, and Reduced Row Echelon Form. Identify free variables, dimension, basics of basis. from Chapter 4: "Systems of Equations as Matrices" in Workbook 21
Determine whether a set of vectors are independent or independent. Understand the basics of a basis and span. from Chapter 5: "Linear Independence and Dependence" in Workbook 21
Understand linear combinations of vectors. from Chapter 3: "Linear Combinations of Vectors" in Workbook 21

Chapter 3: Matrices as Transformations

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Chapter 4: Cross Product

PDF

Objectives

Understand the cross product of two vectors

Video: Cross products | Chapter 10, Essence of linear algebra - YouTube
Video: Cross Product of Two Vectors Explained! - YouTube
Video: 30.2 Cross Product - YouTube
Video: Dot vs. cross product | Physics | Khan Academy - YouTube
Video: Cross product introduction | Vectors and spaces | Linear Algebra | Khan Academy - YouTube
Video: Calculus 3 Lecture 11.4: The Cross Product - YouTube
Video: Right-hand rule for vector cross product - YouTube
Reference: Cross product - Wikipedia
Reference: Vector Calculus: Understanding the Cross Product – BetterExplained
Reference: Orthogonality (mathematics) - Wikipedia
Reference: Triple product - Wikipedia
Reference: 3Blue1Brown - Cross products

Prerequisites

Understand and multiply vectors using the dot product from Chapter 2: "The Dot Product" in Workbook 11
Be able to find the determinant and understand what different values of it mean from Chapter 2: "Determinants and Inverse Matrices" in Workbook 22
Be able to determine the span of vectors in either a line, a plane, or all numbers from Chapter 1: "Span" in Workbook 22

Chapter 5: Applications of Matrices and Systems of Linear Equations

PDF

Objectives

Understand how to apply matrices and systems of linear equations to real life situations

Prerequisites

Understand matrices, vector representations of matrices, dimensions of matrices, scalar matrix multiplication, and the zero matrix and identity matix. from Chapter 2: "Vectors and Matrices" in Workbook 21
Understand linear combinations of vectors. from Chapter 3: "Linear Combinations of Vectors" in Workbook 21
Understand and multiply vectors using the dot product from Chapter 2: "The Dot Product" in Workbook 11
Understand the cross product of two vectors from Chapter 4: "Cross Product" in Workbook 22

Chapter 6: Eigenvectors and Eigenvalues

PDF

Downloads

Python script for creating and using eigenvalues and vectors.

Objectives

Understand how to compute eigenvalues and eigenvectors

Prerequisites

Understand a vector and its properties in depth from Chapter 5: "Vectors" in Workbook 06
Be able to find the determinant and understand what different values of it mean from Chapter 2: "Determinants and Inverse Matrices" in Workbook 22
Understand linear combinations of vectors. from Chapter 3: "Linear Combinations of Vectors" in Workbook 21
Understand and multiply vectors using the dot product from Chapter 2: "The Dot Product" in Workbook 11

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