Select the correct answer(s) about span(A) and the linear least squares problem,Ax b.O any matrix Q whose columns form an orthogonal basis for span(A) is idempotentO for square matrices A, b lies in span(A)the least squares solution occurs when the residual vector is orthogonal to span(A)for overdetermined systems, a solution to least squares is guaranteed to exist

A m×n matrix having m rows and n columns or if it has set of k linear independent vectors in R4,…

Select the correct answer(s) about span(A) and the linear least squares problem, Ax b. O any matrix Q whose columns form an orthogonal basis for span(A) is idempotent O for square matrices A, b lies in span(A) O the least squares solution occurs when the residual vector is orthogonal to span(A) for overdetermined systems, a solution to least squares is guaranteed to exist OO00

Select the correct answer(s) about span(A) and the linear least squares problem, Ax b. O any matrix Q whose columns form an orthogonal basis for span(A) is idempotent O for square matrices A, b lies in span(A) O the least squares solution occurs when the residual vector is orthogonal to span(A) for overdetermined systems, a solution to least squares is guaranteed to exist OO00

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5.5
Which of the following statements is/are correct? Please select one or more: The approximate solution of x1+x2+x3x1x2+αx3=1=1=5 linear equations cannot be found for α=1 by the least squares method. Every set of linear independent vectors in Rn is also an orthogonal set. In Rn, the vector u−projvu is perpendicular to the vector v . If u and v are orthonormal vectors in Rn, ||u+v|| depends on the dimension n. An orthogonal basis for the column space of A is obtained when Gram Schmidt is applied to the column vectors of the linearly independent matrix A with m×n type columns.
7-8. Determine whether the space of the matrix A 2- I 2 O > Am 4 vector ū belongs A₁ = 0 to null
i will 5 upvotes
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.
Only answer the last four please
Prove that the nonzero row vectors of a matrix in row-echelon form are linearly independent. Let = A be an m x n matrix in row-echelon form. If the first column of A is not all zero and e,,, e,m, ean denote leading ones, then the nonzero row vectors r, .. r, of A, have the form of r1 ---Select--- r2 -Select--- ---Select--- and so forth. Then, the equation c,r, + c,r, + ... + cy = 0 implies which of the following equations? (Select all that apply.) U cze3n + C2e3n + Cze3n = 0 C1@2m + Cz€2m = 0 = 0 C1ein + Cz@2n + cze3n Cje im * Cze2m = 0 Cze 3n = 0 Cje11 = 0 You can conclude in turn that c, = c, Ck and so the row vectors are linearly independent.
6) We defined span and looked at the span of a set of vectors geometrically and numerically working with vectors from Rn. When a set of vectors spans a space the linear combination of them generates every object in the space. Can you think of a set of 2x2 matrices such that when you take the span of them you can generate any 2x2 matrix? (hint: think of our standard basis for R2, R3, ... etc.) 7) If you came up with a set of objects in #6 does the set form a basis for the set of all 2x2 matrices? Explain why you think both requirements for a basis are/are not met. 8) What other "objects" have you worked with in mathematics that could potentially form a vector space?
3. Given A= [1 0 (a) Give the vector c so that Ax = b has a solution if and only if b - c = 0. (b) Give a basis of the subspace of all vectors b such that Ax = b has a solution. %3D