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Simultaneous Linear Equations http://nm.mathforcollege.com
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A farmer had 196 cows. When he rounded them up, he had 200 cows. (Reader’s Digest) 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 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/27/9145987/slides/slide_6.jpg "Given then if [C]=[A]-[B], c 23 = A. -3 B. 3 C. 9")
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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/27/9145987/slides/slide_7.jpg "A.-57 B.-45 C.57 D.does not exist 10")
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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/27/9145987/slides/slide_8.jpg "A square matrix [A] is upper triangular if")
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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/27/9145987/slides/slide_9.jpg "B. C. D. all of the above matrix is square 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 a 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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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 on but bad once he/she takes the sunglasses off D. That is what Alejandro calls Lady Gaga E.Slim Shady’s sister! 10 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. A.diagonal B. identity C. lower triangular D. upper triangular http://nm.mathforcollege.com
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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
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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
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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/27/9145987/slides/slide_21.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/27/9145987/slides/slide_22.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/27/9145987/slides/slide_25.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. 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/27/9145987/slides/slide_32.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 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 1. 2. 3. 4. http://nm.mathforcollege.com
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THE END http://nm.mathforcollege.com
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4.09 Adequacy of Solutions http://nm.mathforcollege.com
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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/27/9145987/slides/slide_36.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")
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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/27/9145987/slides/slide_37.jpg "The condition number of a n×n diagonal matrix [A] is A. B. C. D.")
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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/27/9145987/slides/slide_38.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.")
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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/27/9145987/slides/slide_39.jpg "0 B. 1 C. 2 D. 3.")
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THE END http://nm.mathforcollege.com
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