Shreyas’ Notes

# MATH 355

• existence

• uniqueness

• coefficient matrix

• augmented matrix

Linear algebra formalizes the procedure to find all solutions to a linear system of equations when they exist, or to prove that they don’t exist.

### Linear Transformations §

$T : V \rightarrow W$ is a linear transformation if:

• For $u, v \in V$, $T(u + v) = T(u) + T(v)$
• For $v \in V$ and scalar $a$, $T(av) = a \cdot T(v)$

Properties:

• $T(0) = 0$
• any linear transformations respects linear combinations