The purpose of this course is to provide an introduction to linear algebra, a branch of mathematics dealing with matrices and vector spaces. This course describes the use of linear algebra as a compilation of diverse, but interrelated ideas that provide a way of analyzing and solving problems in many applied fields. Linear algebra has three sides: computational techniques, concepts, and applications. One of the goals of this course is to help you master all facets of the subject and see the interplay among them. The material presented in this course involves theorems, proofs, formulas, and computations of various kinds.
Analyze the relationship of linear independence and vector spaces.
Define vector spaces and subspaces.
Apply kernel and range to linear transformations.
Describe matrices as transformations.
Define linear transformations, the geometry of linear operators, and the invertibility of linear transformations.
Identify eigenvalues and eigenvectors.
Apply Cramer’s rule in calculating determinants.
Explain the properties of determinants.
Matrices and Matrix Algebra
Perform matrix factorizations.
Demonstrate inverses of matrices.
Describe operations on matrices.
Systems of Linear Equations
Apply linear systems.
Solve linear systems by row reduction.
Explain systems of linear equations.
Describe vector equations of lines and planes.
Identify dot products.
Explain geometry and algebra of vectors.
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Transferability of credit is at the discretion of the receiving institution. It is the student’s responsibility to confirm whether or not credits earned at University of Phoenix will be accepted by another institution of the student’s choice.