Workbook 22

Chapter 1: Vector Independence

PDF

Downloads

Python script for solving linear equations

Objectives

Understand how to determine of something is linear dependent or independent.

Video: Introduction to linear independence | Vectors and spaces | Linear Algebra | Khan Academy - YouTube
Video: Linear Independence - YouTube
Reference: Linear independence - Wikipedia
Reference: Linear independence - Wikipedia

Prerequisites

Understand linear combinations of vectors. from Chapter 4: "Linear Combinations of Vectors" in Workbook 21

Chapter 2: Span

PDF

Objectives

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

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

Prerequisites

Understand linear combinations of vectors. from Chapter 4: "Linear Combinations of Vectors" in Workbook 21
Understand how to determine of something is linear dependent or independent. from Chapter 1: "Vector Independence" in Workbook 22

Chapter 3: 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: "Span" in Workbook 22
Be able to determine the span of vectors in either a line, a plane, or all numbers from Chapter 2: "Span" in Workbook 22

Chapter 4: 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, matrix multiplication from Chapter 3: "Vectors and Matrices" in Workbook 21
Understand linear combinations of vectors. from Chapter 4: "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 3: "Cross Product" in Workbook 22

Chapter 5: Matrices

PDF

Downloads

Python file for identifying symmetric matrices

Objectives

Understand different types and properties of matrices

Prerequisites

Understand matrices, vector representations of matrices, dimensions of matrices, matrix multiplication from Chapter 3: "Vectors and Matrices" in Workbook 21

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