Standards: Chapter 3

I can determine whether a function T is a linear
transformation. I understand that a linear transformation is
completely determined by its values on e1,e2,…,em and that
every linear transformation can be represented by a unique matrix. I
can graphically represent linear transformations.

Given a linear transformation T, I can determine whether it is
one-to-one and whether it is onto. I understand how a linear
transformation T being one-to-one or onto translates into properties
of the matrix associated to T.

I can perform algebraic operations with matrices, including addition,
subtraction, scalar multiplication, and matrix multiplication. I can
compute the transpose of matrices. I understand the connection between
matrix multiplication and composition of linear transformations.

I can find the inverse of a matrix or determine that no inverse exists
using Gaussian elimination.

I understand what it means for a matrix to be invertible, both
algebraically and conceptually. I understand the relationships among a
matrix being invertible, properties of the associated linear
transformation, and spanning or linear independence properties of the
columns of A (e.g., the Unifying Theorem v. 3).