Number of Solutions to a Linear System

Dot Product

Socks and Shoes Theorem

Number of free variables =

Solution to \(A\vec{x} = \vec{b} \) if \(A\) is invertible

Gaussian Elimination

Reducing to Echelon form options

Inverse of a 2 by 2 Matrix
\[ A =
\begin{bmatrix}
a & b \\
c & d
\end{bmatrix} \]

Vector Space

Nullspace

Linear Combination

Span

Linearly Independent

Basis

Dimension

To determine of vectors are linearly independent...

Cross Product

Equation for plane through two vectors

Column Rank

Row Rank

Rank =

Column Space

dim(CS(A)) =

Basis for CS

To see if \(\vec{b}\) is in CS(A)...