Introduction to Linear Algebra

Linear Algebra is ______

Use Matrices to solve systems of equations

Math Prerequisites: Precalculus, Algebra, Geometry, Trigonometry, Calculus I, Calculus II, Calculus III
The main book used in colleges today is Poole and covers chapters 1-6


[expand title=”1.-Vectors” rel=”submenu-highlander”]

[expandsub2 title=”1.1-The Geometry and Algebra of Vectors” rel=”submenu-highlander1″]

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[expandsub4 title=”Vector Basics – Drawing Vectors/ Vector Addition” rel=”submenu-highlander2″]

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[expandsub4 title=”Vector Basics – Algebraic Representations” rel=”submenu-highlander2″]

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[expandsub4 title=”Vector Basics – Algebraic Representations Part 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Sketching Sums and Differences of Vectors” rel=”submenu-highlander2″]

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[expandsub4 title=”Finding the Components of a Vector, Ex 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Finding the Components of a Vector, Ex 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Vector Addition and Scalar Multiplication, Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Vector Addition and Scalar Multiplication, Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Magnitude and Direction of a Vector, Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Magnitude and Direction of a Vector, Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Magnitude and Direction of a Vector, Example 3″ rel=”submenu-highlander2″]

[embedyt] https://www.youtube.com/watch?v=ZDMm8mtDWhE[/embedyt]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”1.2-Length and Angle: The Dot Product” rel=”submenu-highlander1″]

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[expandsub4 title=”Vectors – The Dot Product” rel=”submenu-highlander2″]

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[expandsub4 title=”An Introduction to the Dot Product” rel=”submenu-highlander2″]

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[expandsub4 title=”Finding a Unit Vector, Ex 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Finding a Unit Vector, Ex 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Word Problems Involving Velocity or Other Forces (Vectors), Ex 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Word Problems Involving Velocity or Other Forces (Vectors), Ex 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Word Problems Involving Velocity or Other Forces (Vectors), Ex 3.” rel=”submenu-highlander2″]

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[expandsub2 title=”1.3-Lines and Planes” rel=”submenu-highlander1″]

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[expandsub4 title=”Finding the Vector Equation of a Line” rel=”submenu-highlander2″]

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[expand title=”2.-Systems of Linear Equations” rel=”submenu-highlander”]

[expandsub2 title=”2.1-Introductlon to Systems of Linear Equations” rel=”submenu-highlander1″]

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[expandsub2 title=”2.2-Direct Methods for Solving Linear Systems” rel=”submenu-highlander1″]

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[expandsub4 title=”Solving a Dependent System of Linear Equations involving 3 Variables ” rel=”submenu-highlander2″]

[embedyt] https://www.youtube.com/watch?v=LNABv0yKA6o[/embedyt]

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[expandsub4 title=”Systems of Linear Equations – Inconsistent Systems Using Elimination by Addition – Example 1″ rel=”submenu-highlander2″]

[embedyt] https://www.youtube.com/watch?v=oGwNLitgbqY[/embedyt]

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[expandsub4 title=”Systems of Linear Equations – Inconsistent Systems Using Elimination by Addition – Example 2″ rel=”submenu-highlander2″]

[embedyt] https://www.youtube.com/watch?v=ZkN_gV4rEuY[/embedyt]

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[expandsub4 title=”Systems of Linear Equations – Inconsistent Systems Using Elimination by Addition – Example 3″ rel=”submenu-highlander2″]

[embedyt] https://www.youtube.com/watch?v=Iptxk7SlvEM[/embedyt]

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[expandsub4 title=”Solving a Dependent System of Linear Equations involving 3 Variables” rel=”submenu-highlander2″]

[embedyt] https://www.youtube.com/watch?v=LNABv0yKA6o[/embedyt]

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[expandsub4 title=”Using Gauss-Jordan to Solve a System of Three Linear Equations – Example 1 ” rel=”submenu-highlander2″]

[embedyt] https://www.youtube.com/watch?v=CsTOUbeMPUo[/embedyt]

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[expandsub4 title=”Using Gauss-Jordan to Solve a System of Three Linear Equations – Example 2 ” rel=”submenu-highlander2″]

[embedyt] https://www.youtube.com/watch?v=Ey62H_oaqoE[/embedyt]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”2.3-Spanning Sets and Linear Independence” rel=”submenu-highlander1″]

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[expandsub4 title=”The Span of a Set of Vectors ” rel=”submenu-highlander2″]

[embedyt] https://www.youtube.com/watch?v=ivP-6oicIWU[/embedyt]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”2.4-Applications” rel=”submenu-highlander1″]

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[expandsub2 title=”2.5-Iterative Methods for Solving Linear Systems” rel=”submenu-highlander1″]

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[expand title=”3.-Matrices” rel=”submenu-highlander”]

[expandsub2 title=”3.0-Introduction: Matrices in Action” rel=”submenu-highlander1″]

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[expandsub2 title=”3.1-Matrix Operations” rel=”submenu-highlander1″]

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[expandsub4 title=”Matrix Operations” rel=”submenu-highlander2″]

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[expandsub2 title=”3.2 Matrix Algebra” rel=”submenu-highlander1″]

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[expandsub2 title=”3.3-The Inverse of a Matrix” rel=”submenu-highlander1″]

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[expandsub2 title=”3.4-The LU Factorization” rel=”submenu-highlander1″]

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[expandsub2 title=”3.5-Subspaces, Basis, Dimension, and Rank” rel=”submenu-highlander1″]

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[expandsub4 title=”Basis for a Set of Vectors” rel=”submenu-highlander2″]

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[expandsub4 title=”Procedure to Find a Basis for a Set of Vectors” rel=”submenu-highlander2″]

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[expandsub2 title=”3.5-Introduction to Linear Transformations” rel=”submenu-highlander1″]

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[expandsub4 title=”Linear Transformations , Example 1, Part 1 of 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Linear Transformations , Example 1, Part 2 of 2″ rel=”submenu-highlander2″]

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[expandsub2 title=”3.7-Applications” rel=”submenu-highlander1″]

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[expand title=”4.-Eigenvalues and Eigenvectors” rel=”submenu-highlander”]

[expandsub2 title=”4.1-Introduction to Eigenvalues and Eigenvectors” rel=”submenu-highlander1″]

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[expandsub4 title=”Finding Eigenvalues and Eigenvectors : 2 x 2 Matrix Example” rel=”submenu-highlander2″]

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[expandsub4 title=”Introduction to Eigenvalues and Eigenvectors – Part 1″ rel=”submenu-highlander2″]

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[expandsub2 title=”4.2-Determinants” rel=”submenu-highlander1″]

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[expandsub4 title=”Determinant of a 2 x 2 Matrix – A Few Basic Questions” rel=”submenu-highlander2″]

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[expandsub4 title=”Determinants to Find the Area of a Triangle” rel=”submenu-highlander2″]

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[expandsub4 title=”Determinants to Find the Area of a Polygon” rel=”submenu-highlander2″]

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[expandsub4 title=”Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Cramer’s Rule to Solve a System of 3 Linear Equations – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Cramer’s Rule to Solve a System of 3 Linear Equations – Example 2″ rel=”submenu-highlander2″]

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[expandsub2 title=”4.3-Eigenvalues and Eigenvectors of nXn Mat rices” rel=”submenu-highlander1″]

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[expandsub2 title=”4.4-Similarity and Diagonalization” rel=”submenu-highlander1″]

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[expandsub2 title=”4.5-Iterative Methods for Computing Eigenvalues” rel=”submenu-highlander1″]

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[expandsub2 title=”4.6-Applications and the Perron-Ferbenius Theorem” rel=”submenu-highlander1″]

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[expand title=”5.-Orthogonality” rel=”submenu-highlander”]

[expandsub2 title=”5.1-Orthogonality in R^n” rel=”submenu-highlander1″]

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[expandsub2 title=”5.2-Orthogonal Complements and Orthogonal Projections” rel=”submenu-highlander1″]

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[expandsub4 title=”Orthogonal Projections – Scalar and Vector Projections” rel=”submenu-highlander2″]

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[expandsub2 title=”5.3-The Gram-Schmidt Process and the QR Factorization” rel=”submenu-highlander1″]

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[expandsub2 title=”5.4-Orthogonal Diagonalization of Symmetric Matrices” rel=”submenu-highlander1″]

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[expandsub2 title=”5.5-Applications” rel=”submenu-highlander1″]

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[expand title=”6.-Vector Spaces” rel=”submenu-highlander”]

[expandsub2 title=”6.1-Vector Spaces and Subspaces” rel=”submenu-highlander1″]

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[expandsub2 title=”6.2-Linear Independence, Basis, and Dimension” rel=”submenu-highlander1″]

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[expandsub4 title=”Linear Independence and Linear Dependence, Ex 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Linear Independence and Linear Dependence, Ex 2″ rel=”submenu-highlander2″]

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[expandsub2 title=”6.3-Change of Basis” rel=”submenu-highlander1″]

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[expandsub2 title=”6.4-Linear Transformations” rel=”submenu-highlander1″]

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[expandsub2 title=”6.5-The Kernel and Range of a Linear Transformation” rel=”submenu-highlander1″]

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[expandsub2 title=”6.6-The Matrix of a Linear Transformation” rel=”submenu-highlander1″]

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[expandsub2 title=”6.7-Applications” rel=”submenu-highlander1″]

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