2A Questions Notes

\(\begin{bmatrix} x_1 & 1 \\ x_2 & 1 \end{bmatrix} * \begin{bmatrix} m \\ b \end{bmatrix} = \begin{bmatrix} y_1 \\ y_2 \end{bmatrix}\)

\(m \cdot x_1+b=y_1\) \(m \cdot x_2+b=y_2\)

can only find lines if they are not colinear

can use determinant to check if lines are colinear
parrel or equal
if it's 0

solve for slopes, simplify, and you get \(0=ad-bc\) damn that's cool!

for example, $

\begin{bmatrix} 1 & 2 \\ 1 & 2 \end{bmatrix}

$ because \(1*2 = 1*2\)

or

$

\begin{bmatrix} 2 & 4 \\ 1 & 2 \end{bmatrix}

$ because \(2*4 = 1*4\)

two axis in 3 space

we listerally have grapher… bro #review play with grapher it's cool

parrell lines which start at 0 are colinear