# Notes - Linear Algebra I MT22, Chapter 7

- [[Course - Linear Algebra I MT22]]
^{U} - Content covered:
**Prove if $B = {} _ {\mathcal{W}}T _ {\mathcal{V}}$ and $A = {} _ {\mathcal{V}}S _ \mathcal{V}$ then $BA = {} _ {\mathcal{W}}TS _ {\mathcal{U}}$. (The. 178)**-
**Prove the change of basis theorem. (Cor. 184)** - Prove a linear system $(A \vert b)$ is consistent if and only if $\text{Col}(A \vert b) = \text{Col}(A)$. (Lem. 190)
**Prove the column rank of a matrix equals its row rank. (The. 191).**