Learning Outcomes

After completing this chapter, students should be able to do the following.

  • 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.