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Workbook 21
Chapter 1: Introduction to Linear Algebra
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Objectives
Understand the concept of linear algebra, matrices, multiplying vector quantities, etc
Prerequisites
Chapter 2: Vectors and Matrices
Objectives
Understand matrices, vector representations of matrices, dimensions of matrices, scalar matrix multiplication, and the zero matrix and identity matix.
Understand how to add, subtract, and multiplication matrices
Understand the basics of how transposition can be simplified using row major or column major order. Relate this idea to computer memory
Prerequisites
Chapter 3: Linear Combinations of Vectors
Objectives
Understand linear combinations of vectors.
Prerequisites
Chapter 4: Systems of Equations as Matrices
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Objectives
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.
Prerequisites
Chapter 5: Linear Independence and Dependence
Objectives
Determine whether a set of vectors are independent or independent. Understand the basics of a basis and span.
Prerequisites
Chapter 6: Subspaces
Objectives
Be able to identify and understand the fundamental subspaces: nullspace, rowspace, and columnspace.
Understand what a nullspace is, its properties, how to find it, and what it can tell us about a matrix A.
Prerequisites
Generated 2026-02-02T11:00.