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Chapter 4 Matrices
Objectives
Perform addition and scalar multiplication of matrices.
Give the dimensions of a matrix product, and compute the product.
Discuss associativity and noncommutativity of matrix multiplication.
Interpret a matrix-vector product as a linear combination of the columns of the matrix.
Employ block multiplication of matrices, when advantageous.
Compute the transpose of a matrix.
Express a solution to a system of linear equations as a sum of a particular solution and a solution to the associated homogeneous system.
Compute the inverse of a matrix using elementary row operations.
Solve systems of linear equations using the inverse of the coefficient matrix, when possible.
Create elementary matrices corresponding to each of the elementary row operations
Solve a system of equations using LU factorization.
