Download presentation
Presentation is loading. Please wait.
1
Simultaneous Linear Equations http://nm.mathforcollege.com
2
The size of matrix A. B. C. D. is 10 http://nm.mathforcollege.com
3
The c 32 entity of the matrix A. 2 B. 3 C. 6.3 D. does not exist 10 http://nm.mathforcollege.com
4
Given then if [C]=[A]+[B], c 12 = A.0 B.6 C.12 10 http://nm.mathforcollege.com
![Given then if [C]=[A]+[B], c 12 = A.0 B.6 C](http://images.slideplayer.com./15/4598462/slides/slide_4.jpg "Given then if [C]=[A]+[B], c 12 = A.0 B.6 C")
5
Given then if [C]=[A]-[B], c 23 = A. -3 B. 3 C. 9 http://nm.mathforcollege.com
![Given then if [C]=[A]-[B], c 23 = A. -3 B. 3 C. 9](http://images.slideplayer.com./15/4598462/slides/slide_5.jpg "Given then if [C]=[A]-[B], c 23 = A. -3 B. 3 C. 9")
6
Given then if [C]=[A][B], then c 31 =. A.-57 B.-45 C.57 D.does not exist 10 http://nm.mathforcollege.com
![Given then if [C]=[A][B], then c 31 =.](http://images.slideplayer.com./15/4598462/slides/slide_6.jpg "A.-57 B.-45 C.57 D.does not exist 10")
7
A square matrix [A] is lower triangular if A. B. C. D. 10 http://nm.mathforcollege.com
![A square matrix [A] is lower triangular if A. B. C. D. 10](http://images.slideplayer.com./15/4598462/slides/slide_7.jpg "A square matrix [A] is lower triangular if A. B. C. D. 10")
8
A square matrix [A] is upper triangular if 1. 2. 3. 4. http://nm.mathforcollege.com
![A square matrix [A] is upper triangular if](http://images.slideplayer.com./15/4598462/slides/slide_8.jpg "A square matrix [A] is upper triangular if")
9
An example of upper triangular matrix is A. B. C. D. none of the above http://nm.mathforcollege.com
10
An example of lower triangular matrix is A. B. C. D. none of the above http://nm.mathforcollege.com
11
An identity matrix [I] needs to satisfy the following A. B. C. D. all of the above matrix is square 10 http://nm.mathforcollege.com
![An identity matrix [I] needs to satisfy the following A.](http://images.slideplayer.com./15/4598462/slides/slide_11.jpg "B. C. D. all of the above matrix is square 10")
12
Given then [A] is a matrix. A.diagonal B. identity C. lower triangular D.upper triangular http://nm.mathforcollege.com
![Given then [A] is a matrix. A.diagonal B. identity C.](http://images.slideplayer.com./15/4598462/slides/slide_12.jpg "lower triangular D.upper triangular")
13
A square matrix is diagonally dominant if 1. 2. 3. 4. http://nm.mathforcollege.com
14
The following system of equations x + y=2 6x + 6y=12 has solution(s). 1.no 2.one 3.more than one but a finite number of 4.infinite 10 http://nm.mathforcollege.com
15
PHYSICAL PROBLEMS http://nm.mathforcollege.com
16
Truss Problem http://nm.mathforcollege.com
17
Pressure vessel problem a b a b c http://nm.mathforcollege.com
18
Polynomial Regression We are to fit the data to the polynomial regression model http://nm.mathforcollege.com
19
END http://nm.mathforcollege.com
20
Simultaneous Linear Equations Gaussian Elimination (Naïve and the Not That So Innocent Also) http://nm.mathforcollege.com
21
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
22
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
23
Increasing the precision of numbers from single to double in the Naïve Gaussian elimination method A.avoids division by zero B.decreases round-off error C.allows equations with a noninvertible coefficient matrix to be solved http://nm.mathforcollege.com
24
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 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://images.slideplayer.com./15/4598462/slides/slide_24.jpg "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")
25
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
![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://images.slideplayer.com./15/4598462/slides/slide_25.jpg "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")
26
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
27
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
28
Simultaneous Linear Equations LU Decomposition http://nm.mathforcollege.com
29
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
30
Truss Problem http://nm.mathforcollege.com
31
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
![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://images.slideplayer.com./15/4598462/slides/slide_31.jpg)
32
If you have n equations and n unknowns, the computation time for forward substitution is approximately proportional to A.4n B.4n 2 C.4n 3 http://nm.mathforcollege.com
33
If you have a n x n matrix, the computation time for decomposing the matrix to LU is approximately proportional to A.8n/3 B.8n 2 /3 C.8n 3 /3 http://nm.mathforcollege.com
34
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
35
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. Now you try to use the Gaussian Elimination method to accomplish the same task. It will now take approximately ____ seconds. A.4 B.64 C.6800 D.27200 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.](http://images.slideplayer.com./15/4598462/slides/slide_35.jpg "Now you try to use the Gaussian Elimination method to accomplish the same task. It will now take approximately ____ seconds. A.4 B.64 C.6800 D")
36
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
![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.](http://images.slideplayer.com./15/4598462/slides/slide_36.jpg "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")
37
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)=at 2 +bt+c to approximate the velocity profile. t(s)01415203035 vm/s0227.04362.78517.35602.97901.67 A. B. C. D. http://nm.mathforcollege.com
38
Three kids-Jim, Corey and David receive an inheritance of $2,253,453. The money is put in three trusts but is not divided equally to begin with. Corey’s trust is three times that of David’s because Corey made and A in Dr.Kaw’s class. Each trust is put in and interest generating investment. The total interest of all the three trusts combined at the end of the first year is $190,740.57. The equations to find the trust money of Jim (J), Corey (C) and David (D) in matrix form is A. B. C. D. http://nm.mathforcollege.com
39
THE END http://nm.mathforcollege.com
40
4.09 Adequacy of Solutions http://nm.mathforcollege.com
41
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
![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://images.slideplayer.com./15/4598462/slides/slide_41.jpg "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")
42
The condition number of a n×n diagonal matrix [A] is A. B. C. D. http://nm.mathforcollege.com
![The condition number of a n×n diagonal matrix [A] is A. B. C. D.](http://images.slideplayer.com./15/4598462/slides/slide_42.jpg "The condition number of a n×n diagonal matrix [A] is A. B. C. D.")
43
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
![The adequacy of a simultaneous linear system of equations [A][X]=[C] depends on (choose the most appropriate answer) A.](http://images.slideplayer.com./15/4598462/slides/slide_43.jpg "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.")
44
If http://nm.mathforcollege.com, then in [A][X]=[C], at least these many significant digits are correct in your solution, A. 0 B. 1 C. 2 D. 3
![If then in [A][X]=[C], at least these many significant digits are correct in your solution, A.](http://images.slideplayer.com./15/4598462/slides/slide_44.jpg "0 B. 1 C. 2 D. 3.")
45
THE END http://nm.mathforcollege.com
46
Consider there are only two computer companies in a country. The companies are named Dude and Imac. Each year, company Dude keeps 1/5 th of its customers, while the rest switch to Imac. Each year, Imac keeps 1/3 rd of its customers, while the rest switch to Dude. If in 2003, Dude had 1/6 th of the market and Imac had 5/6 th of the marker, what will be share of Dude computers when the market becomes stable? 1. 37/90 2. 5/11 3. 6/11 4. 53/90 http://nm.mathforcollege.com
Similar presentations
![SOLVING SYSTEMS OF LINEAR EQUATIONS. Overview A matrix consists of a rectangular array of elements represented by a single symbol (example: [A]). An individual.](/15/4598860/big_thumb.jpg "SOLVING SYSTEMS OF LINEAR EQUATIONS. Overview A matrix consists of a rectangular array of elements represented by a single symbol (example: [A]). An individual.>")
