Download - What is the determinant of 1.9 2.11 3.17 4.19. What is the determinant of 1.0 2.28 3.44 4.-28
What is the determinant of
9 11 17 19
0% 0%0%0%
21
37
1. 9
2. 11
3. 17
4. 19
What is the determinant of
0 28 44 -28
0% 0%0%0%
032
241
026
1. 0
2. 28
3. 44
4. -28
Which matrix represents the following system of equations?
x = 4y = 7
1 2 3
0% 0%0%
71
411.
11112.
710
4013.
What is the solution to the following system of equations?
x1 + x2 = 3 2x1 - 6x2 = -10
x1=
-9/8
and x
2...
x1=
4 an
d x2=
5
x1=
1 an
d x2=
2
x1=
1 an
d x2=
½
Ther
e ar
e an
i...
Ther
e ar
e no
s...
0% 0% 0%0%0%0%
1. x1=-9/8 and x2=-30/8
2. x1=4 and x2=5
3. x1=1 and x2=2
4. x1=1 and x2=½
5. There are an infinite number of solutions
6. There are no solutions
What is the solution to the following system of equations?
6x1 + 9x2 = 32x1 + 3x2 = 5
x1=
2 an
d x2=
0
x1=
0 an
d x2=
1/...
x1=
1 an
d x2=
-1...
x1=
-5/2
and x
2...
Ther
e ar
e an
i...
Ther
e ar
e no
s...
0% 0% 0%0%0%0%
1. x1=2 and x2=0
2. x1=0 and x2=1/3
3. x1=1 and x2=-1/3
4. x1=-5/2 and x2=2
5. There are an infinite number of solutions
6. There are no solutions
Which of the following statements are true?(A) sum of eigenvalues = sum diagonal elements (trace)
(B) product of eigenvalues = determinant of square matrix A(C) distinct eigenvalues = linearly dependent eigenvectors
Only
(A)
Only
(B)
Only
(C)
Both
(A) a
nd (..
.
Both
(A) a
nd (..
.
Both
(B) a
nd (..
.
(A),
(B) a
nd (...
0% 0% 0% 0%0%0%0%
1. Only (A)
2. Only (B)
3. Only (C)
4. Both (A) and (B)
5. Both (A) and (C)
6. Both (B) and (C)
7. (A), (B) and (C)
Which of the following statements is true?
1 2 3 4
0% 0%0%0%
1
eigenvaluean has A 1-
1.
eigenvaluean has k)-(A 2.
1
eigenvaluean has kI)-(A 1-
3.
trueare above theof None4.
Dominant eigenvalue =
eigenvalue with largest magnitude
Tru
e
Fal
se
Don’t
Know
0% 0%0%
1. True
2. False
3. Don’t Know
What is the characteristic equation of the following matrix?
None
of the
ab.
..
0% 0%0%0%
14
26
1. λ² - 7λ + 6 = 0
2. λ² - 7λ + 14 = 0
3. λ² - 7λ - 2 = 0
4. None of the above
What are the eigenvalues of
2 a
nd 4
0 a
nd 4
0 a
nd 2
6 a
nd 8
0% 0%0%0%
20
04
1. 2 and 4
2. 0 and 4
3. 0 and 2
4. 6 and 8
What are the eigenvalues of the following matrix?
0% 0%0%0%
22
48
1. λ = 2, 4
2. λ = 2, 6
3. λ = 2, 8
4. λ = 4, 8
What are the eigenvalues for the following matrix?
0% 0%0%0%
505
055
550
1. λ = -5, 0, 5
2. λ = -5, 5, 10
3. λ = 0, 5, 5
4. λ = 5, 5, 10
What are the eigenvalues for the following matrix?
0% 0%0%0%
1515
030
103
1. λ = -2, 3, 4
2. λ = -6, -2, 3
3. λ = -2, 3, 6
4. λ = -6, -3, 2
Matrix A given below has eigenvalues λ = 2, 4, 6. Without further calculation
write down the eigenvalues for .
1 2 3 4
0% 0%0%0%
-1A
000
131
113
A
3,2,11.
1,1,3
12.
1,3
2,
3
13.
6
1,
4
1,
2
14.
Which of the vectors below is an eigenvector, corresponding to the
eigenvalue λ= 7 of the matrix
1 2 3 4
0% 0%0%0%
54
23
1
2
1.
2
1
2.
1
2
3.
2
1
4.
Which of the vectors below is an eigenvector, corresponding to the
eigenvalue λ= 3 of the matrix
1 2 3 4
0% 0%0%0%
421
130
241
0
1
21.
0
1
22.
0
2
13.
0
2
14.
What are the eigenvectors of the following matrix?
1 2 3 4
0% 0%0%0%
11
55
5
1,
1
11.
5
1,
1
12.
5
1,
1
13.
1
5,
1
14.
Which of the following shows the eigenvectors for matrix A?
1 2 3 4
0% 0%0%0%
200
011
102
A
0
1
3
,
0
1
01.
0
1
3
,
0
1
02.
0
1
1
,
0
1
3
,
0
1
03.
0
1
1
,
0
1
3
,
0
1
04.
Which set of vectors is linearly independent?
(1,6
), (3
,18)
(1,2
), (3
,4)
None
of the
ab.
..
Both
of t
he se
...
0% 0%0%0%
1. (1,6), (3,18)
2. (1,2), (3,4)
3. None of the above
4. Both of the sets
Normalise the eigenvector X.
1 2 3 4
0% 0%0%0%
1
2
3
X
2
122
3
1.
22
12
18
32.
3
13
21
3.
22
24
624.
Diagonalization means which of the following?
Addin
g th
e dia
...
Multi
plyi
ng th...
Tra
nsform
ing
a...
None
of the
ab.
..
0% 0%0%0%
1. Adding the diagonal elements of a matrix.
2. Multiplying the diagonal elements of a matrix.
3. Transforming a non-diagonal matrix.
4. None of the above.
Why might we want to diagonalize a matrix?
Com
puting p
owe...
Eas
y to
find e
...
Both
of t
hese
...
None
of the
se ..
.
0% 0%0%0%
1. Computing powers of the matrix becomes easy.
2. Easy to find eigenvalues of a diagonal matrix.
3. Both of these reasons.
4. None of these reasons
You can always diagonalize an n x n matrix with n distinct
eigenvalues.
Tru
e
Fal
se
Don’t
Know
0% 0%0%
1. True
2. False
3. Don’t Know
Below are eigenvectors of four 2x2 matrices. Which matrix is definitely
diagonalizable?
1 2 3 4
0% 0%0%0%
3
0,
1
01.
3
0,
0
12.
3
1,
3
13.
3
3,
1
14.
Obtain the modal matrix P.
1 2 3 4
0% 0%0%0%
.21
01
A
11
011.
11
012.
11
433.
11
414.
The matrix A= has eigenvalues
-1 and 2 with respective eigenvectors
If calculate .
0% 0%0%0%
20
31
1
1 and
0
1
10
111P
11
1 APP
21
411.
20
212.
20
413.
20
014.
What is A²?
1 2 3 4
0% 0%0%0%
54
32A
108
641.
2516
942.
3728
21163.
4123
23134.
What is ?
1 2 3 4
0% 0%0%0%
54
32A 5A
2520
15101.
31251024
243322.
1423710796
809761403.
809726140
14237107964.
The eigenvalues of a symmetric matrix with real elements are...
Alw
ays
com
plex
Alw
ays
real
Eith
er c
omple
x...
0% 0%0%
1. Always complex
2. Always real
3. Either complex or real
Which of the following is a symmetric matrix?
1 2 3 4
0% 0%0%0%
272
735
2511.
14
412.
473
732
3213.
31
644.
A square matrix A is said to be orthogonal if
True
False
Don’t K
now
0% 0%0%
1. True
2. False
3. Don’t Know
T-1 AA
Two n x 1 column vectors X and Y are orthogonal if XY=0
Tru
e
Fal
se
Don’t
Know
0% 0%0%
1. True
2. False
3. Don’t Know
The eigenvalues of a symmetric matrix A are λ=0 and λ=10
X and Y are the eigenvectors for λ=0 and λ=10 respectively. Are X and Y orthogonal?
0% 0%0%
1. Yes
2. No
3. Don’t Know
13
39A
An Hermitian matrix is one satisfying
True
False
Don’t K
now
0% 0%0%
AAT
1. True
2. False
3. Don’t Know
Is the following matrix Hermitian?
Yes N
o
Don’t
Know
0% 0%0%
1. Yes
2. No
3. Don’t Know
513
102
323
i
i
ii
A
Separating the variables in gives
1 2 3 4
0% 0%0%0%
ss 2
tAets 2)( 1.
sAets 22)( 2.
tAets 22)( 3.
tAets 2)( 4.
Write in matrix form the pair of coupled differential equations
1 2 3 4
0% 0%0%0%
yxy
yxx
5
32
y
x
y
x
13
52
1.
y
x
y
x
13
52
2.
y
x
y
x
15
32
3.
y
x
y
x
15
32
4.
Find the solution of the coupled differential equations
with initial conditions x(0)=1 and y(0)=3
0% 0%0%0%
yy
yxx
3
4
t
tt
ety
eetx3
3
3)(
32)(
1.
t
tt
ety
eetx3
3
3)(
32)(
2.
t
tt
ety
eetx
3)(
32)(
3.
t
tt
ety
eetx
3)(
32)(
4.
Given . What is the general solution to a system of 2nd order differential equations for the
negative eigenvalues ?
1 2 3 4
0% 0%0%0%
21,
tN)sinM(s
tL)cos(Kr
2
1
1.
tNsintMcoss
tLsintKcosr
22
11
2.
tNsintMcoss
tLsintKcosr
21
21
3.
t)sintM(coss
t)sintK(cosr
22
11
4.
rrr 211
An elastic membrane in the plane with boundary circle is
shown below.
21xx12
221 xx
princ
iple
direc
tionprinciple
direction
The membrane is stretched so the point P:( ) goes over the point Q:( ) where
Find the amount that the principle directions are
0% 0% 0%0%0%
21, xx
21, yy
2
1
2
1
74
47
x
xAx
y
yy
stretched by
1. By factors 3 and 11.
2. By factors 7 and 4.
3. By factors 4 and 4.
4. By factors 7 and 7.
5. Don’t Know