Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is...
Transcript of Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is...
![Page 1: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/1.jpg)
1
Simultaneous Linear Equations
http://nm.mathforcollege.com
A farmer had 196 cows. When he rounded them up, he had 200 cows. (Reader’s Digest)
http://nm.mathforcollege.com
![Page 2: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/2.jpg)
2
The name of the person in the picture is
A. A$AP Rocky
B. Kid Cudi
C. MC Hammer
D. T.I.
E. Vanilla Ice
The size of matrix
A.
B.
C.
D.
is
10http://nm.mathforcollege.com
![Page 3: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/3.jpg)
3
The c32 entity of the matrix
A. 2
B. 3
C. 6.3
D. does not exist
10http://nm.mathforcollege.com
Given
then if [C]=[A]-[B], c23=
A. -3
B. 3
C. 9
http://nm.mathforcollege.com
![Page 4: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/4.jpg)
4
Given
then if [C]=[A][B], then c31= .
A. -57
B. -45
C. 57
D. does not exist
10http://nm.mathforcollege.com
A square matrix [A] is upper triangular if
1.
2.
3.
4.
http://nm.mathforcollege.com
![Page 5: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/5.jpg)
5
An identity matrix [I] needs to satisfy the following
A.
B.
C.
D. all of the above
matrix is square
10http://nm.mathforcollege.com
The following system of equations x + y=26x + 6y=12has solution(s).1. no2. one3. more than one but a finite
number of4. infinite
10http://nm.mathforcollege.com
![Page 6: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/6.jpg)
6
PHYSICAL PROBLEMS
http://nm.mathforcollege.com
Truss Problem
http://nm.mathforcollege.com
![Page 7: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/7.jpg)
7
Pressure vessel problem
a
b
a
b
c
http://nm.mathforcollege.com
Polynomial RegressionWe are to fit the data to the polynomial regression model
http://nm.mathforcollege.com
![Page 8: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/8.jpg)
8
END
http://nm.mathforcollege.com
Simultaneous Linear Equations
Gaussian Elimination(Naïve and the Not That So Innocent Also)
http://nm.mathforcollege.com
![Page 9: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/9.jpg)
9
You know Lady Gaga; Who is Shady Gaga
A. Lady Gaga’s sister!
B. A person who looks bad with their sunglasses on.
C. A person who looks good with sunglasses on but bad once he/she takes the sunglasses off
D. That is what Alejandro calls Lady Gaga
E. Slim Shady’s sister!
10http://nm.mathforcollege.com
The goal of forward elimination steps in Naïve Gauss elimination method is to reduce the coefficient matrix to a (an) _________ matrix.
A. diagonal
B. identity
C. lower triangular
D. upper triangular
http://nm.mathforcollege.com
![Page 10: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/10.jpg)
10
One of the pitfalls of Naïve Gauss Elimination method is
A. large truncation error
B. large round-off error
C. not able to solve equations with a noninvertible coefficient matrix
http://nm.mathforcollege.com
Increasing the precision of numbers from single to double in the Naïve Gaussian elimination methodA. avoids division by zero
B. decreases round-off error
C. allows equations with a noninvertible coefficient matrix to be solved
http://nm.mathforcollege.com
![Page 11: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/11.jpg)
11
Division by zero during forward elimination steps in Naïve Gaussian elimination for [A][X]=[C] implies the coefficient matrix [A]
1. is invertible
2. is not invertible
3. cannot be determined to be invertible or not
http://nm.mathforcollege.com
Division by zero during forward elimination steps in Gaussian elimination with partial pivoting of the set of equations [A][X]=[C] implies the coefficient matrix [A]
1. is invertible
2. is not invertible
3. cannot be determined to be invertible or not
http://nm.mathforcollege.com
![Page 12: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/12.jpg)
12
Using 3 significant digit with chopping at all stages, the result for the following calculation is
A. -0.0988
B. -0.0978
C. -0.0969
D. -0.0962
http://nm.mathforcollege.com
Using 3 significant digits with rounding-off at all stages, the result for the following calculation is
A. -0.0988
B. -0.0978
C. -0.0969
D. -0.0962
http://nm.mathforcollege.com
![Page 13: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/13.jpg)
13
Determinants If a multiple of one row of [A]nxn is added or subtracted to another row of [A]nxn to result in [B]nxn then det(A)=det(B)
The determinant of an upper triangular matrix [A]nxn is given by
Using forward elimination to transform [A]nxn to an upper triangular matrix, [U]nxn.
http://nm.mathforcollege.com
Simultaneous Linear Equations
LU Decomposition
http://nm.mathforcollege.com
![Page 14: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/14.jpg)
14
You thought you have parking problems. Frank Ocean is scared to park when __________ is around.
A. A$AP Rocky
B. Adele
C. Chris Brown
D. Hillary Clinton
http://nm.mathforcollege.com
Truss Problem
http://nm.mathforcollege.com
![Page 15: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/15.jpg)
15
If you have n equations and n unknowns, the computation time for forward substitution is approximately proportional toA. 4n
B. 4n2
C. 4n3
http://nm.mathforcollege.com
If you have a nxn matrix, the computation time for decomposing the matrix to LU is approximately proportional to
A. 8n/3
B. 8n2/3
C. 8n3/3
http://nm.mathforcollege.com
![Page 16: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/16.jpg)
16
LU decomposition method is computationally more efficient than Naïve Gauss elimination for solving
A. a single set of simultaneous linear equations
B. multiple sets of simultaneous linear equations with different coefficient matrices and same right hand side vectors.
C. multiple sets of simultaneous linear equations with same coefficient matrix and different right hand side vectors
http://nm.mathforcollege.com
For a given 1700 x 1700 matrix [A], assume that it takes about 16 seconds to find the inverse of [A] by the use of the [L][U] decomposition method. The approximate time in seconds that all the forward substitutions take out of the 16 seconds is
A. 4
B. 6
C. 8
D. 12
http://nm.mathforcollege.com
![Page 17: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/17.jpg)
17
The following data is given for the velocity of the rocket as a function of time. To find the velocity at t=21s, you are asked to use a quadratic polynomial v(t)=at2+bt+c to approximate the velocity profile.
t (s) 0 14 15 20 30 35
v m/s 0 227.04 362.78 517.35 602.97 901.67
1.
2.
3.
4.http://nm.mathforcollege.com
THE END
http://nm.mathforcollege.com
![Page 18: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/18.jpg)
18
4.09Adequacy of Solutions
http://nm.mathforcollege.com
The well or ill conditioning of a system of equations [A][X]=[C] depends on the
A. coefficient matrix only
B. right hand side vector only
C. number of unknowns
D. coefficient matrix and the right hand side vector
http://nm.mathforcollege.com
![Page 19: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/19.jpg)
19
The condition number of a n×n diagonal matrix [A] is
A.
B.
C.
D.
http://nm.mathforcollege.com
http://nm.mathforcollege.com
The adequacy of a simultaneous linear system of equations [A][X]=[C] depends on (choose the most appropriate answer)
A. condition number of the coefficient matrix
B. machine epsilon
C. product of the condition number of coefficient matrix and machine epsilon
D. norm of the coefficient matrix
![Page 20: Simultaneous Linear Equationskaw/download/today/clicker_quiz... · 9 You know Lady Gaga; Who is Shady Gaga A. Lady Gaga’s sister! B. A person who looks bad with their sunglasses](https://reader033.fdocuments.us/reader033/viewer/2022042312/5edb6b6fad6a402d6665a177/html5/thumbnails/20.jpg)
20
If
http://nm.mathforcollege.com
, thenin [A][X]=[C], at least these many significant digits are correct in your solution,
A. 0B. 1C. 2D. 3
THE END
http://nm.mathforcollege.com