precourse.tex

Mv =

\begin{pmatrix}
m_{1,1} \  m_{1,2}
\\ m_{2,1} \  m_{2,2}
\end{pmatrix}

\begin{pmatrix}
v_1
\\ v_2
\end{pmatrix}

=

\begin{pmatrix}
v_1 \times m_{1,1} + v_2 \times m_{1,2}
\\ v_1 \times m_{2,1} + v_2 \times m_{2,2}
\end{pmatrix}

https://latex.codecogs.com/gif.latex?%5Clarge%20Mv%20%3D%20%5Cbegin%7Bpmatrix%7D%20m_%7B1%2C1%7D%20%5C%20m_%7B1%2C2%7D%20%5C%5C%20m_%7B2%2C1%7D%20%5C%20m_%7B2%2C2%7D%20%5Cend%7Bpmatrix%7D%20%5Cbegin%7Bpmatrix%7D%20v_1%20%5C%5C%20v_2%20%5Cend%7Bpmatrix%7D%20%3D%20%5Cbegin%7Bpmatrix%7D%20v_1%20%5Ctimes%20m_%7B1%2C1%7D%20+%20v_2%20%5Ctimes%20m_%7B1%2C2%7D%20%5C%5C%20v_1%20%5Ctimes%20m_%7B2%2C1%7D%20+%20v_2%20%5Ctimes%20m_%7B2%2C2%7D%20%5Cend%7Bpmatrix%7D