Math 202        Study Guide for Chapter #3        C.S. Davis

Your are responsible for the subject matter in sections 3.1-3.4 from the 5th edition of Elementary Linear Algebra by Larson and Edwards. The following topics are the most important. Typical exercises are assigned at the end of each topic. If you need more practice than these, work some more similar exercises.

3.1

1.

Give the definitions of minor, cofactor and determinant. Text

2.

Calculate the determinant of any square matrix by hand and by calculator. P127#1,5,11,15,17,27,49 (all by hand) and 35 (by calculator)

3.

Calculate the determinant of a triangular matrix. P127#41,45

3.2

1.

Apply the theorems about the effect of row or column operations on the value of a determinant and the conditions that make a zero determinant.. P137#1,3,5,7,9

2.

Evaluate a determinant using row or column operations. P137#17,31

3.

Evaluate large sparse determinants. P137#29

4.

Give the determinants of elementary matrices. P138#33,35,37

5.

Prove some easy determinant properties. P138#39,44

3.3

1.

Apply the six theorems from this section. P145#1,5,9,11,15,23,31,45

2.

Apply terms, singular, skew-symmetric and orthogonal. P146#35

3.4

1.

Explain what eigenvalues and eigenvectors are. P152#3

2.

Find the characteristic equation, the eigenvalues and eigenvectors of a given square matrix A. P153#5,11,15

1.

Find the inverse of a matrix A using the adjoint of A. P164#1,3

2.

Use Cramer's rule to solve a system of equations. P164#19,27

3.

Find the area of a triangle, the equation of a line (2 point form) and whether three points are collinear using determinants. P165#41,43,49

4.

Find the volume of a tetrahedron, the equation of a plane (3 point form) and whether four points are coplaner by determinants. P165#51,55,59