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MAT 233 - Linear Algebra - S12

MAT 233 at Franklin College. Spring 2012.

Drew Walters

on 4 February 2013

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Transcript of MAT 233 - Linear Algebra - S12

Orthogonal Vectors Linear Combinations of Vectors 1 2 3 4 Mutliplying Matrices by Vectors Intersection of Lines Linear Transformations Linear Equations
in Linear Algebra Linear Equations in Linear Algebra Solution Method:
Gaussian Elimination The Invertible Matrix Theorem Properties, Sets, and Factorizations

Matrices, Vectors,

Linear Transformations associated with and Determinants Calculation
Cofactors det A=0
iff A is
Singular Geometric
Area & Volume Applications of
Stretching or Shrinking
Caused by
Linear Transformations Properties Chapters 1-2 Chapters 3-4 Chapters 1-2 Chapter 3 Chapter 3 Vector Space Chapter 4 Chapter 4 Chapter 4 Fundamental Subspaces Basis Dimension Rank (30,17) Chapters 3-4 The Invertible Matrix Theorem (Continued...) Eigenvalues & Eigenvectors Diagonalization
A=PDP -1 Orthogonality

Orthonormality Inner Product Norm 1. Orthogonal Vectors
2. Orthogonal Set
3. Orthogonal Basis Chapter 6 Chapter 6 Orthogonal
Complement diasake56(artist). (2010). Hover Board [Digital Media, Paiting]. Retrieved: February 3, 2012, from: http://diasake56.deviantart.com/art/Hover-Board-169484056 openclipart.com (artist). Magic Carpet (Clipart). Retrieved: February 3, 2012, from: http://clipartist.net/tag/magic-carpet/ Broomstick (Clipart). Retrieved: February 3, 2012 from: Microsoft Word 2011. Orthogonal
Projection Gram-Schmidt
Process QR
Matrices Orthogonal
Matrix Least-Squares
Problems Orthogonal Projection
on Subspaces Orthogonal Projection
on Vectors Of Diagonalizable
Segments Quadratic
Forms Symmetric
Matrices Everything is laid out in order of the class, but feel free to move off the path! MAT 233
Linear Algebra
Spring 2012 Built for Updated: February 4, 2013
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