This preview shows page 1. Sign up to view the full content.
SAMPLE MIDTERM II
MATH 54 SEC.1, FALL 2009
80 POINTS, 80 MINUTES
Question 1, 18 pts
True or false? No justiFcation necessary. Correct answers carry 1
.
5 points,
incorrect answers carry 1
.
5 points penalty. However, you will not receive a negative total score on
any group of 6 questions.
T ±
If
A
is diagonalizable, then so is
A
2
.
T ±
The columns of a diagonalizable matrix are linearly independent.
T ±
If
A
is an
n
×
n
diagonalizable matrix, then each vector in
R
n
can be written as
a linear combination of eigenvectors of
A
.
T ±
If the square matrix
A
is singular, then 0 must be an eigenvalue of
A
.
T ±
The eigenvalues of an upper triangular matrix are exactly the diagonal entries.
T ±
Each eigenvector of an invertible matrix
A
is also an eigenvector of
A

1
.
T ± A vector
v
and its negative

v
have equal lengths.
T ± If
u
and
v
are orthogonal, then

u
+
v

2
=

u

2
+

v

2
.
T ± If
λ
is a real eigenvalue of the orthogonal matrix
A
, then
λ
=
±
1.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/10/2010 for the course MATH 54 taught by Professor Chorin during the Fall '08 term at University of California, Berkeley.
 Fall '08
 Chorin
 Math

Click to edit the document details