# Mathematical and Computational Methods in Physics and Engineering (fall 2016)

## Daily outline for Fri, Sep 23, 2016 9:10 AM (1 year ago)

### Linear Algebra 2

assigned today:
• standard-linear vector spaces:

I can determine the rank of a matrix and whether vectors are linearly independent.

1. Prove that any 3 non-zero 2d vectors are linearly dependent.
2. Prove that the determinant of a system equations (not all of which equal zero) that has multiple solutions is zero.
3. 7.7.20 (a) and (b).

Due today:
• standard-matrices and gaussian elimination:

I can manipulate matrices and solve systems of linear equations.

1. 7.2.28
2. Explain figure 158
3. 7.3.17

# plan

• linear independence and spanning the space
• reinterpretation of the matrix equation
• determinant
• specifically an all zero row
• matrix inversion

# in class

• quiz on Markov
• we talked a lot about it afterwards
• 3 vectors in 2d that come back to origin
• had to say that they needed to have a net non-zero contribution
• 2 vectors to get to a random point in 2d
• discussed similarities between those two approaches
• talked about homogeneous (too many solutions)
• talked about determinant and how it helps find if it's homogeneous
• kind of ran out of time to pull it all together

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