Linear Algebra II: Matrix Algebra

Upon completion of this course, learners will be able to:

• Apply matrix algebra, the matrix transpose, and the zero and identity matrices, to solve and analyze matrix equations.
• Apply the formal definition of an inverse, and its algebraic properties, to solve and analyze linear systems.
• Characterize the invertibility of a matrix using the Invertible Matrix Theorem.
• Apply partitioned matrices to solve problems regarding matrix invertibility and matrix multiplication.
• Compute an LU factorization of a matrix and apply the LU factorization to solve systems of equations.
• Apply matrix algebra and inverses to solve and analyze Leontif Input-Output problems.
• Construct transformation matrices to represent composite transforms in 2D and 3D using homogeneous coordinates.
• Construct a basis for a subspace.
• Calculate the coordinates of a vector in a given basis.
• Characterize a matrix using the concepts of rank, column space, and null space.
• Apply the Rank, Basis, and Matrix Invertibility theorems to describe matrices, subspaces, and systems.