Linear Algebra notes

Matrices are like funcitions that transform a vector

for example multiplying: $\left[\begin{array}{cc}1& 2\\ 2& 3\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]$ This is changing the bases vectors i and j of a vector to i be in $[1,2]$ and j be $[2,3]$

I and J are basis vectors

Column Space: All possible outputs of a Matrix multiplication A x v, since A matrix changes the basis vectors, it will result in a new span

Rank: Number of dimensions in a column space

Keywords:

1. Gaussian Elimination