1: T!e or Fa!. (Plese sl]rport yoq Nd
cfw_ith s bief reMr or a counter exarpl. )
ls Lei M be d n x n motrix, Il lhe .olums of ill de ind.pmdeDt then ihe kch.l ol
M is just ihc zdo ve.tor.
\ r "l
r ',.r F -)
+ r .Mq - - ( .
Notes 23: More Eigenvalues, Eigenvectors
Lecture December 8, 2010
Given a 2 2 matrix M with complex eigenvalues, our goal is to nd a basis B of R2
so that the matrix representing M with respect to the basis B is simple. Indeed we will
show how to nd a bas
Notes 22: More Eigenvalues, Eigenvectors
Lecture December 6, 2010
We apply our algorithms for nding eigenvalues and eigenvectors to 3 3 matrices. To
do this we need a dierent way of calculating the determinants of matrices. it is called
expansion by minor
Math 235 section 1 r Midterm 1 Spring 2014
This is a 90 minutes exam. This exam paper consists of 6 questions. It has 7 pages.
The useof calculators is not allowed on this exam. You may use one letter size page of
More review problems on applications
1. Suppose that the air pressure of air leaking out of a leaky tire loses
pressure at a rate proportional to the pressure dierence between the
current air pressure in the tire and the ambient pressure of the surroundin
Math 235 Sections 01 and 02
Intro to Linear Algebra
This document is only a summary. More information, updates, and any
changes will be posted on the course-wide and/or section webpages.
Math 235 Section 01 (Class Number 74711)
1. Vector spaces
(1) Define vector space: V is a vector space if .
(2) Define vector subspace: W is a subspace of a vector space V if .
(3) Determine which of the following sets are vector subspaces.
(g) cfw_p(t) 2 P2 : p(t) = p( t)
: x 0, y 0
( F( ) )
t : )
C1t s 1
Math 331: Dierential Equations
Solutions of midterm 2A
Department of Mathematics and Statistics
University of Massachusetts
Question 1: Find the general solution of the given dierential equation.
(a) y 00 + 4y 0 + 5y = 0
(b) 6y 00 y 0 y = 0.