Simultaneous Linear Equations

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