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Simultaneous Linear Equations http://nm.mathforcollege.com
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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
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The size of matrix A. B. C. D. is 10 http://nm.mathforcollege.com
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The c 32 entity of the matrix A. 2 B. 3 C. 6.3 D. does not exist 10 http://nm.mathforcollege.com
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Given then if [C]=[A]+[B], c 12 = 1.0 2.6 3.12 10 http://nm.mathforcollege.com
![Given then if [C]=[A]+[B], c 12 =](http://images.slideplayer.com/16/5254958/slides/slide_5.jpg "Given then if [C]=[A]+[B], c 12 =")
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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/16/5254958/slides/slide_6.jpg "A square matrix [A] is lower triangular if A. B. C. D. 10")
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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/16/5254958/slides/slide_7.jpg "B. C. D. all of the above matrix is square 10")
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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/16/5254958/slides/slide_8.jpg "A.-57 B.-45 C.57 D.Does not exist 10")
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The following system of equations x + y=2 6x + 6y=12 has solution(s). 1.no 2.one 3.more than one but finite number of 4.infinite 10 http://nm.mathforcollege.com
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PHYSICAL PROBLEMS http://nm.mathforcollege.com
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Truss Problem http://nm.mathforcollege.com
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Pressure vessel problem a b a b c http://nm.mathforcollege.com
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Polynomial Regression We are to fit the data to the polynomial regression model http://nm.mathforcollege.com
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END http://nm.mathforcollege.com
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Simultaneous Linear Equations Gaussian Elimination (Naïve and the Not That So Innocent Also) http://nm.mathforcollege.com
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The goal of forward elimination steps in Naïve Gauss elimination method is to reduce the coefficient matrix to a (an) _________ matrix. 1.diagonal 2. identity 3. lower triangular 4. upper triangular http://nm.mathforcollege.com
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One of the pitfalls of Naïve Gauss Elimination method is 1.large truncation error 2.large round-off error 3.not able to solve equations with a noninvertible coefficient matrix http://nm.mathforcollege.com
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Increasing the precision of numbers from single to double in the Naïve Gaussian elimination method 1.avoids division by zero 2.decreases round-off error 3.allows equations with a noninvertible coefficient matrix to be solved http://nm.mathforcollege.com
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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/16/5254958/slides/slide_19.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")
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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/16/5254958/slides/slide_20.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")
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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
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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
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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/16/5254958/slides/slide_23.jpg)
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Simultaneous Linear Equations LU Decomposition http://nm.mathforcollege.com
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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
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Truss Problem http://nm.mathforcollege.com
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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
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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
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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
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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/16/5254958/slides/slide_30.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")
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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/16/5254958/slides/slide_31.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")
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THE END http://nm.mathforcollege.com
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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
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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 but bad once he/she takes the sunglasses off D. That is what Alejandro calls Lady Gaga 10 http://nm.mathforcollege.com
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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/16/5254958/slides/slide_35.jpg "lower triangular D.upper triangular")
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A square matrix is diagonally dominant if 1. 2. 3. 4. 5. http://nm.mathforcollege.com
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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
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An example of upper triangular matrix is A. B. C. D. none of the above http://nm.mathforcollege.com
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An example of lower triangular matrix is A. B. C. D. none of the above http://nm.mathforcollege.com
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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
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Is how much you are loaded up related to test score? http://nm.mathforcollege.com
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Final Grade vs Test#1 Grade http://nm.mathforcollege.com
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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/16/5254958/slides/slide_43.jpg)
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The name of the person in the picture is A.Yung Joc B.Kid Cudi C.T.I. D.MC Hammer http://nm.mathforcollege.com
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Kanye West is a genius except A.He grabbed Taylor Swift’s mike at the VMAs B.Has diamonds drilled to his bottom teeth C.Sings about Mama’s boyfriend D.All of the above http://nm.mathforcollege.com
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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
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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
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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/16/5254958/slides/slide_48.jpg "Given then if [C]=[A]-[B], c 23 = A. -3 B. 3 C. 9")
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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/16/5254958/slides/slide_49.jpg "A square matrix [A] is upper triangular if")
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