Please look at the formula sheet which will be included with Exam 3 and also with the Final Exam for your reference.
Which of the four subspaces are the orthogonal complements of which and what it means for a subspace to be the orthogonal complement of another.
How to find the orthogonal projection of b onto the subspace C(A).
How to find x that minimizes ||Ax-b||.
Given a set of vectors how to find a set of orthonormal vectors that span the same subspace.
Properties of orthogonal matrices Q.
How to compute the determinant of a triangular matrix.
How to compute determinant of A by using the LU decomposition of A.
How to compute the determininant of a permutation matrix.
How to compute 2x2 and 3x3 determinants using the combinatorial formula.
How to use Cramer's rule to solve the system Ax=b.
How to find the inverse of A in terms of the cofactor matrix and the determinant of A.