Linear Algebra Summary Notes

• Determine linear (in)dependence
  • Let $c_1,c_2\in \mathbb{R}$ satisfying $c_1\mathbf{u}+c_2\mathbf{v}=0⟹$

$$\left[\begin{array}{c}{u}_1{c}_1+v_1{c}_2\\ u_2{c}_1+v_2{c}_2\end{array}\right]=\left[\begin{array}{c}0\\ 0\end{array}\right]⟹\dots$$

• Find two nontrivial vectors that span the plane
  • Any two linearly independent vectors (aren’t multiples of one another).