REVIEW PROBLEMSFINAL EXAM (Brief solutions)
1. Cauchy-Schwarz inequality: |u v| u v
triangle inequality: u + v u + v .
Assume Cauchy-Schwarz. Then
u + v 2 = (u + v) (u + v) = u 2 + 2u v + v 2 u 2 + 2 u v + v 2 = ( u + v )2 .
REVIEW PROBLEMSFINAL EXAM
Note: This problem set concentrates on material from the end of the course. For a complete review, you
should also study the review problem sets for the two in-class exams. Please consider these
EXAM 2: REVIEW PROBLEMS
1. In each part below give the precise denition in one or more full sentences.
(a) The span of a set of vectors S = cfw_u1 , . . . , uk ;
(b) A linearly independent set of vectors S = cfw_u1 , . . . , uk ;
(c) A subspace o
640:250 Linear Algebra
EXAM 1: REVIEW PROBLEMS (Brief Solutions)
rev. 20 Jan. 2014
1. (a) Every column of A is a pivot column, so if Ax = 0 then x = 0.
(b) rref(A) is the identity matrix, so A has pivot in every column. Hence S is independent.
2. (b) Yes:
Matlab Assignment #1
LAB 1: Matrix and Vector Computations in Matlab
In this lab you will use Matlab to study the following topics:
How to create matrices and vectors in Matlab.
How to manipulate matrices in Matlab and creat