Have an understanding of vector spaces. 4. Be able to solve eigenvalue problems. I is to review systems of equations, matrix representation of systems of equations, and applications of systems of equations. Students are introduced to geometric vectors, vector operations, vector equations, and matrix equations in the context of coordinate spaces. Ideas studied include coordinate equations, parametric equations, spanning sets, linear independent sets, and linear dependence.
Students learn to add, subtract, multiply, invert, and transpose matrices.
Scalar multiplication is introduced and students learn properties that express relationships between all operations. Properties of invertible matrices that unify the content of linear algebra are identified. Determinants are introduced and used to describe solutions to systems of equations. Matrices are both partitioned and factored. This unit abstracts the idea of vector space.