Math 337 -Midterm Exam 1-Spring 2011
1.(25 points) Consider the linear system
x1 x2 x3 + 2 x4 = 1
2x1 2x2 x3 + 3x4 = 3
x1 + x2 x3 = 3.
a) Find the general solution in the form x = xp + xh of the system. Indicate
free and basic variables.
b) Find the pivot
MATH 337 -FINAL EXAM-SPRING 2011
Justify all your answers.
1.(15 points) a) Let A = [v1 v2 v3 v4 ], where v1 = (1, 0, 1)T , v2 = (3, 0, 3)T , v3 =
(0, 1, 1)T , v4 = (2, 4, 6)T , and b = (1, 6, 7)T . Find the general solution of Ax=b.
b) Are the columns of
1
In each case compute the error as the Euclidian norm | A - LU|.
1. Let A be a tridiagonal matrix that is either diagonally dominant or positive definite. Write MATLAB's
function [L, U] = trilu(a, b, c) that computes the LU factorization of A. Here a, b,
Math 337 Sample Exam Instructions. This sample exam is provided as an aid for preparing for the first midterm exam. Additionally, preparation for the midterm exam should include review of lectures, quizzes and all assigned homework problems. Problem 1. Su
Math 337 Fall 2004 Midterm Examination 1 Instructions. Show your work. Calculators are not permitted. Scoring: 12 points per problem, except problem 8 which is 16 points (parts of problems are equally weighted unless noted otherwise). This examination has
M ATH
3 37 _ F INAL
E XAM
_ F ALL 2 011
Show all work a.ndjustify all steps of each argument you make.
1 ) ( 2 0p o i n t s )L e t A :
f u p 2 u s u aw i t h o r : ( 1 , 2 , 3 ) r , u 2 : ( 2 , 4 , 6 ) T , , t ) s :
l
(3,8,7)", u a : ( 5,12,1 3)", a nd b
Math 337 -Midterm Exam 2-Spring 2011
1.(25 points) a) Find the LU factorisation of A = [v1 v2 v3 ], where v1 = (1, 2, 1)T , v2 =
(3, 8, 3)T , v3 = (1, 4, 4)T .
b) Use part a) to nd det(A) and detL100 .
c) Use part a) to solve the system Ax = b with b = (4
M ATH 3 37-FINAL E XAM
M ay 1 2, 2 010
1 . ( 1 5p o i n t s )L e t u 1 - ( 1 , - 1 , 5 ) r , u z : ( - 4 , 2 , - 6 ) 7 , , u 3 :
(-7, 1 ,7)? b e t he c olumnso f t he m atrix . 4.
( g ,- 4 , 1 0 ) r , u a :
a) F ind b asesf or N ul(A), C ot(A), a nd R ow(
Math 337 -FINAL EXAM -December 15, 2010
Show all work and justify all steps of each argument you make.
1)(20 points) Let A = [v1 v2 v3 ] with v1 = (2, 1, 1)T , v2 = (0, 8, 2)T and
v3 = (6, 5, 1)T and b = (10, 3, 3)T .
a) Are the columns of A linearly inde
Final E xarn
A
M ath 3 37-Linear lgebra
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