March 1, 2018

Assigned seating. Your individualized paper has your UBIT username on the front page. They will be laid out alphabetically by UBIT username.

Will need to bring your ID.

Points awarded for "style".

rank A = dim Col A

Rank theorem: rank A + dim Nul A = n

Basis theorem: If dim H = p, any LI set of vectors in H is a basis for H. And any spanning set of p vectors in H is a basis for H.

More observations about ad-bc for

a b c d

to 3x3 and higher.

Motivation (3.3): observations about determinant in Strang house - meaning?

reflections, rotations, scrunch, etc.

Ideas:

- should be zero if there's a zero row
- flip sign if rows swapped
- multiplication of a single row (or column)
- no change if multiple of one row added to other

a_{11} |
a_{12} |
a_{13} |

a_{21} |
a_{22} |
a_{23} |

a_{31} |
a_{32} |
a_{33} |

Expansion by minors

cofactors

Determinant of a triangular matrix

Determinant via row-reduction

Determinant of transpose

Determinant of product AB, proof via writing A as product of elementary matrices

Answer some of the exercises in the book.