MATH. 20F SAMPLE MIDTERM 2
You have
50 minutes
for this exam. Please write legibly and show all
working.
No calculators are allowed.
Write your name and ID number.
Name:
ID Number:
(1i)
(5 points) Find the determinant of
A
=
1
0
0
1
2
0
1
0
11 3
7
5
0
0

1 0
.
Calculate the determinant by using cofactor expansion along the 2nd col
umn and then the 3rd column:
det
A
=

3
·
det
1
0
1
2
1
0
0

1 0
=

3
·
1
·
det
p
2
1
0

1
P
= (

3)
·
1
·
(

2) = 6
(ii) (5 points) If
A
is an
n
×
n
matrix, how are det(3
A
) and det(
A
) related?
The matrix 3
A
is obtained from
A
by multiplying each row by 3. Each
such ERO multiplies the determinant by 3. Hence
det(3
A
) = 3
n
·
det(
A
)
.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
MATH. 20F SAMPLE MIDTERM 2
(2i) (10 points) Let
P
2
be the vector space of polynomials of degree
≤
2,
and let
W
=
{
p
∈
P
2
:
p
(0) +
p
′
(1) = 0
}
.
Show that
W
is a subspace of
P
2
and Fnd a basis for
W
.
It is clear that the zero polynomial is in
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '03
 BUSS
 Linear Algebra, Algebra, Determinant, Vector Space, λ, 50 Minutes, MATH. 20F SAMPLE, 20F SAMPLE MIDTERM

Click to edit the document details