This course provides a survey of the concepts related to linear algebra. Students examine the geometry of vectors, matrices, and linear equations, including Gauss-Jordan elimination. Students explore the concepts of linear independence, rank, and linear transformations. Vector spaces, bases, and change of bases are discussed, including orthogonality and the Gram–Schmidt process. In addition, students investigate determinants, eigenvalues, and eigenvectors.
Examine applications of linear algebra using Leontief’s closed model.
Determinants, Orthogonality, Eigenvalues, and Eigenvectors
Evaluate eigenvalues and eigenvectors using the characteristic polynomial.
Decompose a vector space into its subspace and orthogonal complement.
Calculate the dot, or inner, product of two vectors.
Extrapolate abstract vector spaces from specific vector spaces.
Determine the basis and dimension of a subspace of Rn.
Determine the kernel and range of the matrix representation of a subspace of Rn.
Vectors and Linear Transformations
Use linear transformations to transform a vector from Rn to Rm.
Transform vectors in two- and three-dimensional spaces using matrices.
Determine a spanning set for independent vectors.
Solve applications of linear systems.
Simplify vectors into linear combinations using vector algebra.
Linear Equations and Matrix Algebra
Determine the invertibility of a matrix.
Perform matricial calculations.
Solve linear equations using Gauss-Jordan elimination.
Solve systems of linear equations with m equations and n unknowns.
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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.