Math 321 Linear Algebra

Course Information

• Instructor: Cristina Pereyra
• Email: crisp at math dot unm dot edu
• Office: Humanities 459
• Schedule: Tue, Th 2:00-3:15pm, Room DSH 229
• Website: [1]

Notes

• Math 321 2010-01-19
• Linear-Algebra-2010-02-02
• Linear-Algebra-2010-02-04

Audio

• Linear-Algebra-2010-02-02.m4a
• Linear-Algebra-2010-02-04.m4a

Assignments

Assignment 1

Remedial

• Solving Linear Systems with Gauss' Method
  • (1) an equation is swapped with another
  • (2) an equation has both sides multiplied by a nonzero constant
  • (3) an equation is replaced by the sum of itself and a multiple of another

Review

Sections 3.1 and 3.2

We can perform three elementary row/column operations on matrices to identify linear dependencies, and invertibility. The three operations are:

1. Swap any two rows/columns.
2. Multiply any row/column by a non-zero scalar.
3. Add any non-zero scalar multiple of a row/column to another row/column.

• All of the above mentioned operations are invertible.
• The sum of two nxn elementary matrices is a elementary matrix
• The same matrix X is obtainable by both a set of row and a set of column operations.

• Both elementary row and column operations preserve rank.
• The rank of a matrix is equal to the maximum number of linearly independent rows in the matrix
• An n x n matrix having rank n is invertible.

Determining the existence of an inverse

Given some matrices A the Identity Matrix I, and the augmented matrix (A|I), if we can transform the A portion via elementary row operations into I, then the mutually transformed right hand side (our original I portion) will be equal to the inverse of our original A.

• If at some point we obtain a row of all zeros on the left hand side, then A does not have an inverse.