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

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 http://nm.mathforcollege.com

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

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

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

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

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

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

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

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

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

Given then [A] is a matrix. diagonal identity lower triangular upper triangular http://nm.mathforcollege.com

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

The following system of equations x + y=2 6x + 6y=12 has solution(s). no one more than one but a finite number of infinite 10 http://nm.mathforcollege.com

PHYSICAL PROBLEMS http://nm.mathforcollege.com

Truss Problem http://nm.mathforcollege.com

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

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

END http://nm.mathforcollege.com

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

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

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

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

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

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

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

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

Simultaneous Linear Equations LU Decomposition http://nm.mathforcollege.com

You thought you have parking problems 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

Truss Problem 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://nm.mathforcollege.com 32

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

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

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

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

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

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) 14 15 20 30 35 v m/s 227.04 362.78 517.35 602.97 901.67 http://nm.mathforcollege.com

Three kids-Jim, Corey and David receive an inheritance of $2,253,453 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

THE END http://nm.mathforcollege.com

4.09 Adequacy of Solutions http://nm.mathforcollege.com

coefficient matrix only right hand side vector only number of unknowns The well or ill conditioning of a system of equations [A][X]=[C] depends on the coefficient matrix only right hand side vector only number of unknowns coefficient matrix and the right hand side vector http://nm.mathforcollege.com

The condition number of a n×n diagonal matrix [A] is http://nm.mathforcollege.com

condition number of the coefficient matrix machine epsilon The adequacy of a simultaneous linear system of equations [A][X]=[C] depends on (choose the most appropriate answer) condition number of the coefficient matrix machine epsilon product of the condition number of coefficient matrix and machine epsilon norm of the coefficient matrix http://nm.mathforcollege.com

If , then in [A][X]=[C], at least these many significant digits are correct in your solution, 1 2 3 http://nm.mathforcollege.com

THE END http://nm.mathforcollege.com

Consider there are only two computer companies in a country 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

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

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

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

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

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

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

This Kiss – Faith Hill It's a feeling like this It's centrifugal motion It's perpetual bliss It's that pivotal moment It's, ah unthinkable This kiss, this kiss Unsinkable This kiss, this kiss http://nm.mathforcollege.com