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110.201 Linear Algebra
5th Quiz
April 22, 2005
Problem 1
Using determinant rules, ﬁnd the determinant of the matrix
A
=
1 1 1
1
1 4 4
4
1 4 9
9
1 4 9 16
.
Problem 2
True or false, with reason if true and counterexample if false:
1. If A and B are identical except in the upperleft corner, where
b
11
= 2
a
11
,
then det
B
= 2det
A
.
2. The determinant of a matrix is the product of the pivots.
3. If A is invertible and B is singular, then
A
+
B
is invertible.
4. If A is invertible and B is singular, then
AB
is singular.
Problem 3
An invertible linear map
L
:
R
n
→
R
n
is called orientation
preserving if det(
A
)
>
0, and orientation reversing otherwise.
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This homework help was uploaded on 01/23/2008 for the course MATH 201 taught by Professor Consani during the Spring '05 term at Johns Hopkins.
 Spring '05
 CONSANI
 Linear Algebra, Algebra, Determinant

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