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
TRANSCRIPT
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What is the determinant of
9 11 17 19
0% 0%0%0%
21
37
1. 9
2. 11
3. 17
4. 19
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What is the determinant of
0 28 44 -28
0% 0%0%0%
032
241
026
1. 0
2. 28
3. 44
4. -28
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Which matrix represents the following system of equations?
x = 4y = 7
1 2 3
0% 0%0%
71
411.
11112.
710
4013.
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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
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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
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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)
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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.
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Dominant eigenvalue =
eigenvalue with largest magnitude
Tru
e
Fal
se
Don’t
Know
0% 0%0%
1. True
2. False
3. Don’t Know
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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
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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
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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
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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
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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
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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
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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
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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.
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Obtain the modal matrix P.
1 2 3 4
0% 0%0%0%
.21
01
A
11
011.
11
012.
11
433.
11
414.
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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.
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What is A²?
1 2 3 4
0% 0%0%0%
54
32A
108
641.
2516
942.
3728
21163.
4123
23134.
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What is ?
1 2 3 4
0% 0%0%0%
54
32A 5A
2520
15101.
31251024
243322.
1423710796
809761403.
809726140
14237107964.
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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
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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.
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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
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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
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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
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An Hermitian matrix is one satisfying
True
False
Don’t K
now
0% 0%0%
AAT
1. True
2. False
3. Don’t Know
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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
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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.
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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.
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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.
![Page 39: 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](https://reader030.vdocuments.mx/reader030/viewer/2022032703/56649f515503460f94c73e8f/html5/thumbnails/39.jpg)
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
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An elastic membrane in the plane with boundary circle is
shown below.
21xx12
221 xx
princ
iple
direc
tionprinciple
direction
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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