1 / 49

Simultaneous Linear Equations

Simultaneous Linear Equations. The name of the person in the picture is. A$AP Rocky Kid Cudi MC Hammer T.I. Vanilla Ice. The size of matrix. is. 10. The c 32 entity of the matrix. 2 3 6.3 does not exist. 10. Given. 0 6 12. then if [C]=[A]+[B], c 12 =. 10.

norman
Download Presentation

Simultaneous Linear Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Simultaneous Linear Equations http://nm.mathforcollege.com

  2. The name of the person in the picture is • A$AP Rocky • Kid Cudi • MC Hammer • T.I. • Vanilla Ice

  3. The size of matrix is 10 http://nm.mathforcollege.com

  4. The c32 entity of the matrix • 2 • 3 • 6.3 • does not exist 10 http://nm.mathforcollege.com

  5. Given • 0 • 6 • 12 then if [C]=[A]+[B], c12= 10 http://nm.mathforcollege.com

  6. A square matrix [A] is lower triangular if 10 http://nm.mathforcollege.com

  7. An identity matrix [I] needs to satisfy the following matrix is square all of the above 10 http://nm.mathforcollege.com

  8. Given • -57 • -45 • 57 • Does not exist then if [C]=[A][B], then c31=. 10 http://nm.mathforcollege.com

  9. The following system of equations x + y=26x + 6y=12has solution(s). • no • one • more than one but finite number of • infinite 10 http://nm.mathforcollege.com

  10. PHYSICAL PROBLEMS http://nm.mathforcollege.com

  11. Truss Problem http://nm.mathforcollege.com

  12. a a c b b Pressure vessel problem http://nm.mathforcollege.com

  13. Polynomial Regression We are to fit the data to the polynomial regression model http://nm.mathforcollege.com

  14. END http://nm.mathforcollege.com

  15. Simultaneous Linear EquationsGaussian Elimination(Naïve and the Not That So Innocent Also) http://nm.mathforcollege.com

  16. The goal of forward elimination steps in Naïve Gauss elimination method is to reduce the coefficient matrix to a (an) _________ matrix. • diagonal • identity • lower triangular • upper triangular http://nm.mathforcollege.com

  17. One of the pitfalls of Naïve Gauss Elimination method is • large truncation error • large round-off error • not able to solve equations with a noninvertible coefficient matrix http://nm.mathforcollege.com

  18. Increasing the precision of numbers from single to double in the Naïve Gaussian elimination method • avoids division by zero • decreases round-off error • allows equations with a noninvertible coefficient matrix to be solved http://nm.mathforcollege.com

  19. Division by zero during forward elimination steps in Naïve Gaussian elimination for [A][X]=[C] implies the coefficient matrix [A] • is invertible • is not invertible • cannot be determined to be invertible or not http://nm.mathforcollege.com

  20. 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] • is invertible • is not invertible • cannot be determined to be invertible or not http://nm.mathforcollege.com

  21. Using 3 significant digit with chopping at all stages, the result for the following calculation is • -0.0988 • -0.0978 • -0.0969 • -0.0962 http://nm.mathforcollege.com

  22. Using 3 significant digits with rounding-off at all stages, the result for the following calculation is • -0.0988 • -0.0978 • -0.0969 • -0.0962 http://nm.mathforcollege.com

  23. 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]nxnis given by Using forward elimination to transform [A]nxnto an upper triangular matrix, [U]nxn. http://nm.mathforcollege.com

  24. Simultaneous Linear EquationsLU Decomposition http://nm.mathforcollege.com

  25. You thought you have parking problems. Frank Ocean is scared to park when __________ is around. • A$AP Rocky • Adele • Chris Brown • Hillary Clinton http://nm.mathforcollege.com

  26. Truss Problem http://nm.mathforcollege.com

  27. If you have n equations and n unknowns, the computation time for forward substitution is approximately proportional to • 4n • 4n2 • 4n3 http://nm.mathforcollege.com

  28. If you have a nxn matrix, the computation time for decomposing the matrix to LU is approximately proportional to • 8n/3 • 8n2/3 • 8n3/3 http://nm.mathforcollege.com

  29. LU decomposition method is computationally more efficient than Naïve Gauss elimination for solving • a single set of simultaneous linear equations • multiple sets of simultaneous linear equations with different coefficient matrices and same right hand side vectors. • multiple sets of simultaneous linear equations with same coefficient matrix and different right hand side vectors http://nm.mathforcollege.com

  30. 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. • 4 • 64 • 6800 • 27200 http://nm.mathforcollege.com

  31. 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 • 4 • 6 • 8 • 12 http://nm.mathforcollege.com

  32. THE END http://nm.mathforcollege.com

  33. Consider there are only two computer companies in a country. The companies are named Dude and Imac. Each year, company Dude keeps 1/5th of its customers, while the rest switch to Imac. Each year, Imac keeps 1/3rd of its customers, while the rest switch to Dude. If in 2003, Dude had 1/6th of the market and Imac had 5/6th of the marker, what will be share of Dude computers when the market becomes stable? • 37/90 • 5/11 • 6/11 • 53/90 http://nm.mathforcollege.com

  34. You know Lady Gaga; Who is Shady Gaga • Lady Gaga’s sister • A person who looks bad with their sunglasses on • A person who looks good with sunglasses but bad once he/she takes the sunglasses off • That is what Alejandro calls Lady Gaga 10 http://nm.mathforcollege.com

  35. Given • diagonal • identity • lower triangular • upper triangular then [A] is amatrix. http://nm.mathforcollege.com

  36. A square matrix is diagonally dominant if http://nm.mathforcollege.com

  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)=at2+bt+c to approximate the velocity profile. http://nm.mathforcollege.com

  38. An example of upper triangular matrix is none of the above http://nm.mathforcollege.com

  39. An example of lower triangular matrix is none of the above http://nm.mathforcollege.com

  40. 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 http://nm.mathforcollege.com

  41. Is how much you are loaded up related to test score? http://nm.mathforcollege.com

  42. Final Grade vs Test#1 Grade http://nm.mathforcollege.com

  43. 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]nxnis given by Using forward elimination to transform [A]nxnto an upper triangular matrix, [U]nxn. http://nm.mathforcollege.com

  44. The name of the person in the picture is • Yung Joc • Kid Cudi • T.I. • MC Hammer http://nm.mathforcollege.com

  45. Kanye West is a genius except • He grabbed Taylor Swift’s mike at the VMAs • Has diamonds drilled to his bottom teeth • Sings about Mama’s boyfriend • All of the above http://nm.mathforcollege.com

  46. Example of a Poem Boom Boom Pow, That is how I feel when I come to class, Glad that I have a lot of mass. I need to integrate my work and life, Differentiate between love and strife, Interpolate when my friend whines, Isn’t that same as reading between the lines? http://nm.mathforcollege.com

  47. This Kiss – Faith Hill It's a feeling like thisIt's centrifugal motionIt's perpetual blissIt's that pivotal momentIt's, ah unthinkableThis kiss, this kissUnsinkableThis kiss, this kiss http://nm.mathforcollege.com

  48. Given • -3 • 3 • 9 then if [C]=[A]-[B], c23= http://nm.mathforcollege.com

  49. A square matrix [A] is upper triangular if http://nm.mathforcollege.com

More Related