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ENEE 241 02*
HOMEWORK ASSIGNMENT 5
Due Tue 02/24
Problem 5A
(i) (10 pts.)
Let
A
2
1
0
=
u
,
A
1
2
0
=
v
and
A
1
1
1
=
w
,
where
u
,
v
and
w
are
m
×
1 vectors.
Determine the dimensions of the matrix
A
and express each of its columns in terms of
u
,
v
and
w
.
For the remainder of this problem, consider the following two transformations on the (
x,y
) plane:
•
B
: counterclockwise rotation by 45
◦
;
•
C
: stretch in the horizontal (
x
) direction by a factor of 2; no stretch in the vertical (
y
)
direction.
(ii) (4 pts.)
Determine the corresponding matrices
B
and
C
.
(iii) (3 pts.)
Show that
BC
6
=
CB
.
(iv) (3 pts.)
Verify the result of (iii) above by sketching (on two separate ﬁgures) the result of
applying
BC
and
CB
to all points on the unit square (whose vertices are (0
,
0), (0
,
1), (1
,
0) and
(1
,
1)).
Problem 5B
Let
A
=
a b c
0
d e
0
f
r
0
s
t
0
u v w
In each of the following cases, ﬁnd matrices
P
and
Q
such that
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