Linear Algebra
Section 3.1 : Spaces of vectors
Section 3.2 : The Nullspace of A : Solving Ax=0
Monday, March 4th
Math 301
Week #7
1
Monday, March 4, 13
Goal of Chapter 3
Determine the solvability of a linear system, and
characterize their solution.
We wil
Linear Algebra
Section 3.3 : The Rank and Row Reduced Form
Section 3.4 : The Complete Solution to Ax=b
Monday, March 11th
Math 301
Week #8
1
Tuesday, March 12, 13
Matrix rank
The true size of a matrix is determine by the rank of
a matrix.
The rank r of a
Linear Algebra
Section 4.3 : Linear least squares
Wednesday March 20th
Math 301
Week #9
1
Tuesday, March 26, 13
Least squares approximation
Suppose b is not in the column space of A. Then can
we nd a best solution to Ax = b?
b
Project b onto the column sp

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Linear Algebra
Section 3.5 : Independence, Basis and Dimensions
Section 3.6 : Dimensions of the four subspaces
Wednesday, March 13th
Math 301
Week #8
1
Thursday, March 14, 13
Linear independence
A set of vectors (v1 , v2 , . . . , vN ) are linearly indepe
Linear Algebra
Section 2.6 : LU Decomposition
Section 2.7 : Permutations and transposes
Wednesday, February 13th
Math 301
Week #4
1
Saturday, February 23, 13
The LU Decomposition
We learned last time that we can factor a invertible
matrix as
A = LU
where