# Math 220 Material

**FINAL EXAM TIME AND LOCATION:**

April 30 (Monday) at 2:30- 4:20pm in 111 Forum Building

**For the Final Exam the student should know the following topics:**

Systems of linear equations, row reduction algorithm, linear combinations, span, determine if a vector belong to the span of given vectors, linear independence/dependence of vectors, linear subspaces, linear systems as matrix equations, describe geometrically the solution of a linear system, homogeneous linear systems, linear transformations and their matrices, operations on matrices, find the inverse of a matrix if it exists, invertible matrices and its criteria, determinant of a square matrix, properties of determinants, Cramer’s rule, basis of a subspace, coordinates of a vector in a given basis, dimension of a subspace, rank of a matrix, column space and null space, eigenvectors and eigenvalues of a matrix, characteristic polynomial of a square matrix, diagonalization of a square matrix, dot product and its properties, length of a vector, distance between two vectors, orthogonal/orthonormal set of vectors, orthogonal/orthonormal basis, orthogonal matrix, orthogonal projections on a line and a subspace, find distance from a point to a given subspace, find coordinates of a vector in a given orthogonal basis, Gram-Schmidt algorithm, symmetric matrices, find orthogonal diagonalization of a symmetric matrix.

**Class time and location:**

** MATH 220.011** – MW 9:05-9:55 am in 101 Osmond Laboratory.

** MATH 220.013** – MW 10:10-11:00 am in 316 Nursing Sciences Building.

**Office hours: **Monday 2-3pm and Friday 9:30-11am in 016 McAllister Building and by appointment.

**Contact information: *** e-mail:* axe930 “AT” psu “dot” edu.

**REVIEW SESSIONS for final exam:**

*Review with me*: April 28 (Saturday) at 12:20-3:20pm in 101 Osmond Laboratory

*Review with Penn State Learning*: April 28 (Saturday) at 2:30-4:30pm in 102 Thomas Building

**Some useful information:**

Sample Final Exams – Solutions: Fall 2012, Spring 2008, Fall 2004

Final Exam Fall 2011 – Solution: Fall 2011

Some Review Problems with Solutions

Sample exams

Fall 2016 Midterm

Fall 2016 Midterm Makeup

Lecture notes from the publisher – We covered the following sections: 1.1 – 1.5, 1.7 – 1.9, 2.1 – 2.3, 2.8 – 2.9, 3.1 – 3.3, 5.1 – 5.3, 6.1 – 6.4, 7.1