MA 341 REVIEW SHEET FOR TEST 3

• Take the practice test at www4.ncsu.edu/~lakurtz/341.html

• 9.3 Review: Matrices and Algebra

-Know basic matrix operations (addition, multiplication, finding inverses of 2x2s and 3x3s, finding determinants of 2x2s and 3x3s)

-Understand what it means for a matrix to be a solution to a matrix differential equation

- ex. p. 547-549 (p. 521-522 O.B.) #1,4, 9,11,13,17,21,25,37

• 9.4 Linear Systems in Normal Form

-Write systems of equations in matrix form

-ex. p. 556-557 (p. 530 O.B.) #1-11 odd

• 9.5 Homogeneous Linear Systems with Constant Coefficients

-Given a matrix find its eigenvalues and eigenvectors

-Find the general solution (Remember for a 3x3 matrix I’ll give you the eigenvalues)

-Examples p. 567-568 (p. 541-542 O.B.) # 1,5,16,32

-Look at 9.5 Worksheet

• 9.6 Complex Eigenvalues

-Know the form of the general solution if we have complex eigenvalues

-Examples p. 575 (p. 549 O.B.) # 1,3,13

-Look at 9.6 Worksheet

• 9.7 Nonhomogeneous Linear Systems

-Know the method of Variation of Parameters

-Examples p.581 (p. 555 O.B.) # 1,3,11,13,15,21a

• 5.1/5.2 More practice solving systems of equations

-Be able to set up an interconnected tank problem

-Examples p. 271 (p 251 O.B.) #31 and problems we’ve worked in class

-Look at Mixing Problems with Interconnected Tanks Worksheet