Assignment Section_7.3_Eigenvalues_Eigenvectors due 09/29/2021 at 11:59pm MST
Problem 1. (1 point)
Find the eigenvalues and eigenvectors of the matrix A =
[ -; -� ]
"-1 = -, v1 = [ =
]
and
"-2=-,v2= [ =]
Answer(s) submitted:
• -1
(correct)
Problem 2. (1 point)
Find the eigenvalues and eigenvectors of the matrix A =
[ =; =!
]
"-1 = -, v1 = [ =
]
and
"-2=-,v2= [ =]
Answer(s) submitted:
•-1
(correct)
Problem 3. (1 point)
Let _ [ -3 ] _ [ 3 ] _ [0 ]
v1 = _ 1 , v2 = _4 , v3 = 5 .
Are the vectors v1 , v2 and v3 linearly independent?
•choose
•linearly dependent
•linearly independent
If the vectors are independent, enter zero in every answer blank
since those are only the values that make the equation below true.
If they are dependent, find numbers, not all zero, that make the
equation below true. You should be able to explain and justify
your answer.
[ � ] = - [ =
� ] + - [ �4 ] + - [ � ] .
Answer(s) submitted:
•linearly dependent
•1
(correct)
Problem 4. (1 point)
Let ,, -[ �3 l
, .; -[ �: J , % - [ �2 l
Are the vectors v1, v2 and v3 linearly independent?
•choose
•linearly dependent
•linearly independent
If the vectors are independent, enter zero in every answer blank
since zeros are only the values that make the equation below true.
If they are dependent, find numbers, not all zero, that make the
equation below true. You should be able to explain and justify
your answer.
[
i l [ �3
l +-[ �: l +-[ +
l
Answer(s) submitted:
•linearly dependent
•-2
(correct)
Problem 5. (1 point)
Let v,-[ n ,<;-[ n%-[ n
Are the vectors v1, v2 and v3 linearly independent?
•choose
•linearly dependent
•linearly independent
If the vectors are independent, enter zero in every answer blank
since zeros are only the values that make the equation below true.
If they are dependent, find numbers, not all zero, that make the
equation below true. You should be able to explain and justify
your answer.
[il [n+-[n+-[H
Answer(s) submitted:
•linearly independent
• 0
(correct)
Problem
6.
(1
point)
Let
2
—2t
0
—g
—2t
x)=
|
ear]
x=
[yea]
x0=|
"5
|
Are
the
vectors
x‘!)(t),
x(2)(t)
and
x)
(r)
linearly
independent?
¢
choose
¢
linearly
dependent
¢
linearly
independent
If
the
vectors
are
independent,
enter
zero
in
every
answer
blank
since
those
are
only
the
values
that
make
the
equation
below
true.
If
they
are
dependent,
find
numbers,
not
all
zero, that
make
the
equation
below
true.
You
should
be
able
to
explain
and
justify
your
answer.
3-22-19]
Generated
by
OWeBWork,
http://webwork.maa.org,
Mathematical
Association
of
America
Answer(s)
submitted:
e
linearly
dependent
e
4
(correct)
Problem
7.
(1
point)
6
-l
LetA=|
_
9 k
Determine
the
value
of
k
for
which
the
matrix
is
singular
(i.e.
not
invertible).
k=__
Solution:
SOLUTION
The
matrix
is
singular
if
det(A)
=
0.
We
have
det(A)
=
6k
—
9,
thus
the
matrix
is
singular
if
k
=
2.
Answer(s)
submitted:
e@
(3/2)
(correct)
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