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Linear Algebra Review Problems for First ExamSolutions
1.(12 points) Find all solutions to the following system of linear equations
3
x
1 2 1
2 1 1 y = 1
0
z
75 2
Solution: Represent as a matrix and row reduce:
1 2 1
2 1 1
75 2
1 2 1
0 3 3
0 9 9
1 2 1
Linear Algebra Review Problems for Final Exam
Note: The nal will consist of 100 points with roughly equivalent point assignments.
1.(20 points)
101
Given A = 0 1 0
111
(a) Compute the characteristic polynomial of A.
(b) Find the eigenvalues of A.
(c) Find
Linear Algebra Review Problems for First Exam
Note: This practice test is longer than the actual examThe actual exam will total 100 pts,
with roughly the same values as assigned here. Hopefully actually this isnt too much review.
1.(12 points) Find all so
Name:
Linear Algebra Quiz 4
June 19, 2006
1.(20 points)
220
Given A = 2 2 0
004
(a) Compute the characteristic polynomial of A.
(b) Compute the eigenvalues of A.
(c) Find a basis for R3 consisting of eigenvalues of A.
(d) Find an invertible matrix P and a
Name:
Linear Algebra Quiz 3
June 13, 2006
1.
2
1
3
2
,
and = cfw_
,
.
1
1
1
1
(a)(4 points) Find the transition matrices from -coordinates to standard coordinates, coordinates to standard coordinates, and -coordinates to -coordinates, i.e., nd [id]STD ,
Name:
Linear Algebra Quiz 2
June 5, 2006
4
1
1
1.(10 points) Is the set cfw_ 2 , 3 , 6 linearly independent or dependent? Ex2
2
1
plain.
2.(10 points) Consider the set S of all 3 3
the form
ab
0 d
00
upper triangular matrices, i.e., matrices of
c
e
f
S
Ok check it out. I think this is right:
d1 (ej )(ek , el ) = ek ej (el ) + ej (ek )el + ej (ek el )
i
i
i
i
(using Einstein notation)
m
= ek il ej + ik ej el + ej (Tkl em )
i
i
n
n
= il Tkj en + ik Tjl en + Tkl ej
(without Einstein)
j
j
i
n
n
= n=j (il Tk
Name:
Linear Algebra Quiz 4.2
June 20, 2006
1.(20 points)
4 2
11
(a) Compute the characteristic polynomial of A.
(b) Compute the eigenvalues of A.
(c) Find a basis for R2 consisting of eigenvalues of A.
(d) Find an invertible matrix P and a diagonal matri
Linear Algebra Homework 3 Selected Solutions
Note: Any mistakes are the sole responsibility of the authorT.Peters
3.6.12 Let A be a 4 5 matrix. If a1 , a2 , a4 are linearly independent and
a3 = a1 + 2a2 and a5 = 2a1 a2 + 3a4 determine RREF(A).
Heres an ex
Linear Algebra S2010D Sec.1, Summer 2006
Final Exam
Name:
June 27, 2006
Do all problems, in any order.
Show your work. An answer alone may not receive full credit.
No notes, texts, or calculators may be used on this exam.
Problem Possible Points
Points Ea
Name:
Linear Algebra Extra Credit for Final Exam
June 13, 2006
The following problems may be done for extra credit on the nal exam. More will be added
as time goes on. These problems will be due on Friday June 23 at 5PM. Same policy as last
timeplease han
Linear Algebra Extra Credit Problems
May 31, 2006
The following problems may be done for extra credit on the rst exam. Normally I encourage everyone to work together on homeworks but since this is
for extra credit Id prefer if you work on your own. This a
Linear Algebra S2010D Sec.1, Summer 2006
Exam 1
Name:
June 9, 2006
Do all problems, in any order.
Show your work. An answer alone may not receive full credit.
No notes, texts, or calculators may be used on this exam.
Problem
Possible Points
Points Earned