3. LetA =101020000 02200-2 2, and b=112314(a) Factor A into a product QR, where is an orthogonal matrix and R is upper triangular.(b) Solve linear system Ax = b for the least squares solution using Q and R.

Answered: Image /qna-images/answer/1a94bc4c-2e9e-4d61-90b6-19996d025aa2.jpg

Answered: 3. Let A 1 0 1 0 2 0 0 0 2 0 0 2 0 0-2…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

3 Using matrix diagonalisation, solve the following system of first order difference equations: Xn+1 = 6xn + Yn Yn+1 = 5x + 2yn with initial conditions to = 1 and yo = -1.
Do 2b)
Suppose that Ax=b has no solution and the columns of A are linearly independent. Let t(A) denote the transpose of matrix A. Select all true statements. O If the A matrix and b vector represent data values, then the least-squares solution gives coefficients for a function that make this function the line that best fits the data values. O The system has a least-squares solution. The solution to t(A)Ax=t(A)b is the least-squares solution. O In the system Ax-b=e, it is possible for e to be the zero vector. O The system has a least squares solution but it may not be unique. O The inverse of t(A)A exists. O The least-squares solution (if it exists) yields a vector in the column space of A that is the "closest" to the vector b.
2. For which h the matrix 1 1 -1 h 1 1 2 1 A 1 has two pivot columns?
Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b. 14 HA A = - 18 b= 1 14 7 4 a. The orthogonal projection of b onto Col A is b = (Simplify your answers.)
1. In each part of this question, you have been given a system of equations and the corresponding matrix taken to RREF. Write the general solution as a vector equation. • List the basic solutions. a. b. (x₁ - x₂ + 2x4 = 0 [1 -X₁ + x₂ + 3x3 - 11x4 0 2x₁ - 2x₂ + 4x4 0 0 -4x₁ + 4x₂ + 3x3 - 17x4 = 0 Lo - = 0 " -1 0 2 01 0 1 -3 0 0 0 0 0 0 00 (3w+9y15z = 0 1 0 -14w + 33x - 75y - 62z = 0 0 1 -5w+ 14x - 29y - 31z = 0 0 0 (52w 164x + 320y + 396z = 0 Lo 0 3 -1 -4 0 0
can you please solve this question ( 1.5.6) ?
Consider the problem of finding a quadratic polynomial p(x) which best fits the data (-1,0),(0,1),(1,2),(2,4). b the four equations p(-1) = 0, p(0) = = = (a) Write in matrix form Ac : 1,p(1) = 2, p(2) = 4. (b) Is there a solution c to the matrix equation Ac = b in part (a)? (c) Write down the normal equation of Ac = b. (d) Without calculating the solutions to this normal equation, explain why it must have at least one solution.
Solve the given set of equations by applying L-U decomposition method. The upper triangular matrix U should include 1’s on its diagonal. -2.2a-5.72b-2.64c=-11.44 2.5a+4.1b+9.72c=1.576 -a-0.5b-5.68c=3.116
By using the method of least squares, find the best line through the points: (−2,−1), (2,1), (0,–3). Step 1. The general equation of a line is c + ₁ = y. Plugging the data points into this formula gives a matrix equation Ac = y. Step 2. The matrix equation Ac = y has no solution, so instead we use the normal equation ATA ĉ = A¹y ATA= ATy = Step 3. Solving the normal equation gives the answer Ĉ= which corresponds to the formula y = Analysis. Compute the predicted y values: y ŷ = Compute the error vector: e=y-ŷ. = Aĉ. Compute the total error: SSE = e² + e² + ez. SSE =
5x1 + 6x2 + 11x3 + 7x4 6x5 5 4. Membership in a Span: For every item: (i) apply the Modified Gauss-Jordan Algorith to determine if b is in Span(S); (ii) write the solution vector i if there are solutions to ti corresponding augmented matrix; (iii) express S in the simplest possible way, and check directly that your answer is correct. as a linear combination of the vectors а. Б - (-4, 2, -3); S - {{7,4, -6), (-5, -2, 3)} b. b = (-4, 2,–4); S = {(7,4,–6), (-5,–2, 3)} %3| b = (9, 7,-8, 2); S = {(5,-3, 2, 6), (-2,–3, 5, 8), (–5, 4,–2,–3)} d. b = (-10, 13,–4, 9); S = {(5,-3, 2, 6), (-5, 4,–2,–3), (-5, 7,–2, 6)} Б - (13, 14,-18,-11); S = {(5,-3, 2, 6), (–2,–3, 5, 8), (–5, 4,–2,–3), (11, 10,–13,-6)} b = (8,–9,–8, 15,-3), S = {(6,0,4, 3, 2), (3, 2, 7, 1,–2), (2, 1, 2, –1, 3)} b = (-4,–1, 4, 7,-9), S = {(3, 2, 7, 1,–2), (2, 1, 2,–1, 1), (1, 0,–3,–3, 4)} h. Б - (-3,6, -1,-9, 4), S = {(6,0,–1, 3, 2), (3, 2,–3, 1,–2), (0,–4, 5, 1, 6), (3,–2, 1, 3, 3)} с. %3D е. f. g.
Let A be a 3 x 3 matrix with two pivot positions. Does the equation Ax = 0 have nontrivial solutions? Explain. Yes. Since A has two pivots, there is one free variable. So Ax = 0 has nontrivial solutions. O No. Since A has two pivots, there is one free variable. Since there is at least one free variable, Ax: O has only the trivial solution. Yes. Since A has two pivots, there is one free variable. The solution set of Ax O does not contain the trivial solution if there is at least one free variable. AR O No. Since A has two pivots, there are no free variables. With no free variables, O has only the trivial solution. Ax

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

3. Let A 1 0 1 0 2 0 0 0 2 0 0 2 0 0-2 2 1 and b = 11 2 3 14 (a) Factor A into a product QR, where Q is an orthogonal matrix and R is upper triangular. (b) Solve linear system Ax = b for the least squares solution using Q and R.