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The following notes are originally from a Math 284 class from Spring 2017.

Notes of Feb 14 - 2.3 Spanning sets and linear independence

Notes of Feb 16 - 2.3 Linear independence

Notes of Feb 21 - 2.3 Linear independence, 3.1 Matrix operations

Notes of Feb 23 - 3.1 Partitioned matrices, 3.2 Matrix algebra

Notes of Feb 28 - 3.2 Linearly independent matrices, 3.3 Inverse of a matrix

Notes of Mar 2 - 3.3 Elementary matrices, Fundamental Theorem of Invertible Matrices

Notes of Mar 7 - 3.3 Gauss-Jordan elimination to find the inverse of a matrix

Notes of Mar 9 - 3.5 Subspaces, row space, column space of a matrix

Notes of Mar 14 - 3.5 Null space, row space, column space

Notes of Mar 16 - 3.5 Null space, row space, column space (continued); how to do Quiz 2 (not in notes)

Mar 21 - How to do much of Quiz 3 (not in notes)

Mar 23 - *Test 1* on Chapter 2 and 3.1 through 3.5

Notes of Apr 4 - 3.5 Fundamental Theorem of Invertible Matrices, 3.6 Intro to linear transformations

Notes of Apr 6 - 3.6 Intro to linear transformations, 6.1 Vector spaces and subspaces

Notes of Apr 11 - 6.1 More examples of vector spaces, 6.2 Linear independence, basis, dimension

Notes of Apr 13 - 6.2 Linear independence, basis, dimension

Notes of Apr 18 - 6.2 Coordinates of a vector with respect to a basis

Notes of Apr 20 - 6.4 Linear transformations

Notes of Apr 25 - 6.5 Kernel and range of a linear transformation

Notes of Apr 27 - Sample exercises from sections 6.1, 6.2, and 6.4

Notes of May 2 - 6.5 ker(T) = {0} if and only if T is one-to-one

May 4 - 6.5 V is isomorphic to W iff dim V = dim W; Intro to 6.6 Matrix of a linear transformation

Notes of May 9 - 6.6 Matrix of a linear transformation

Notes of May 11 - 4.1 Intro to eigenvalues, eigenvectors; 4.2 Determinants; Sample exercises from 6.5

Notes of May 16 - 4.1 Eigenvectors and eigenvalues for a square matrix A

Notes of May 18 - 4.2 Determinants: det(AB) = (det A)(det B)

May 23 - 4.3 Eigenvalues and eigenvectors of a square matrix

**Supplemental notes** from Fall 2017:

Sep 28 - 3.5 Coordinates relative to a basis

Oct 31 - more 6.5 and 6.6 homework exercises

Nov 2 - 6.3 Change of basis matrix

Nov 7 - continuation of Oct 31 exercises

Nov 16 - 4.3 Finding eigenvectors, eigenvectors

Nov 21 - 4.4 Diagonalization

Nov 28 - 4.4 Similar matrices

Nov 30 - 5.1 Orthogonality in R^n

**Supplemental notes** from Spring 2018:

Feb 12 - Two vectors are linearly dependent iff one is a scalar multiple of the other

Feb 26 - Factoring a matrix as a product of elementary matrices and its rref

Mar 7 - Find row(A), col(A), null(A): an exercise from 3.5

Apr 16 - How to come up with your own basis for a vector space (section 6.2)

Apr 18 - One-to-one and onto transformations (end of section 6.5)

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