CS512  Homework 0 (0%)
Due by: September 5, 2017
submit via bitbucket
(A)
Let:
A
=
⎡
⎢
⎢
⎢
⎣
1
2
3
⎤
⎥
⎥
⎥
⎦
,
B
=
⎡
⎢
⎢
⎢
⎣
4
5
6
⎤
⎥
⎥
⎥
⎦
,
C
=
⎡
⎢
⎢
⎢
⎣
− 1
1
3
⎤
⎥
⎥
⎥
⎦
, find:
2
A
−
B

A

and the angle of
A
relative to the positive
X
axis
Â
, a unit vector in the direction of
A
the direction cosines of
A
A
⋅
B
and
B
⋅
A
the angle between
A
and
B
a vector which is perpendicular to
A
A
×
B
and
B
×
A
a vector which is perpendicular to both
A
and
B
the linear dependency between
A
,
B
,
C
A
^{T}
B
and
A
B
^{T}
.
(B)
Let:
A
=
⎡
⎢
⎢
⎢
⎣
1
2
3
4
− 2
3
0
5
− 1
⎤
⎥
⎥
⎥
⎦
,
B
=
⎡
⎢
⎢
⎢
⎣
1
2
1
2
1
− 4
3
− 2
1
⎤
⎥
⎥
⎥
⎦
,
C
=
⎡
⎢
⎢
⎢
⎣
1
2
3
4
5
6
− 1
1
3
⎤
⎥
⎥
⎥
⎦
, find:
2
A
−
B
AB
and
BA
(
AB
)
^{T}
and
B
^{T}
A
^{T}

A

and

C

(note A10)
the matrix (
A
,
B
, or
C
) in which the row vectors form an orthogonal set
A
^{ − 1}
and
B
^{ − 1}
(note B5)
(C)
Let:
A
=
⎡
⎢
⎣
1
2
3
2
⎤
⎥
⎦
,
B
=
⎡
⎢
⎣
2
− 2
− 2
5
⎤
⎥
⎦
, find:
the eigenvalues and corresponding eigenvectors of
A
.
the matrix
V
^{ − 1}
AV
where
V
is composed of the eigenvectors of
A
.
the dot product between the eigenvectors of
A
.
the dot product between the eigenvectors of
B
.
the property of the eigenvectors of
B
and its reason (note C4).
(D)
Let:
f
(
x
) =
x
^{2}
+ 3
,
g
(
x
,
y
) =
x
^{2}
+
y
^{2}
, find:
the first and second derivatives of
f
(
x
)
with respect to
x
:
f
’(
x
)
, and
f
’’(
x
)
.
the partial derivatives:
(
∂
g
)/(
∂
x
)
, and
(
∂
g
)/(
∂
y
)
.
the gradient vector
∇
g
(
x
,
y
)
.
the probability density function (pdf) of a univariate Gaussian (normal) distribution.
Submission instructions
Prepare your solution in a pdf file (either type and export to pdf, or hand write and scan/photograph).
Create a free bitbucket account or use your existing account if you have one (http://bitbucket.org).
Create a PRIVATE repository
cs512f17FIRSTLAST
where FIRST/LAST are your first/last name.
Share this repository (give read permission) with
cs512iit
Inside your repository create a folder called AS0 and upload your assignment file there.