Homework Answers
7. Consider the following matrix (a) Find the QR decomposition of A using the Gram Schmidt process. (b) Use the QR deco...
7. Consider the following matrix (a) Find the QR decomposition of A using the Gram Schmidt process. (b) Use the QR decomposition from (a) to find the least-squares solution to Ax = b where -3
7. Consider the following matrix (a) Find the QR decomposition of A using the Gram Schmidt process. (b) Use the QR decomposition from (a) to find the least-squares solution to Ax = b where -3
== 2 1 3 (1 point) Let A 1 and b -3 2 6 The QR...
== 2 1 3 (1 point) Let A 1 and b -3 2 6 The QR factorization of the matrix A is given by: 1 2 = ſ v2 ŠV2 0 V2 3 2 3 (a) Applying the QR factorization to solving the least squares problem Ax b gives the system: 3 wls, wie X = (b) Use backsubstitution to system in part (a) and find the least squares solution. =
2 9 11 and b (1 point) Let A -6 The QR factorization of the matrix...
2 9 11 and b (1 point) Let A -6 The QR factorization of the matrix A is given by: 2 1 6 17 äv2 3 1 1 0 3 2 3 21 V2 3 áva (a) Applying the QR factorization to solving the least squares problem Ax b gives the system: X = 0 2 3 (b) Use backsubstitution to solve the system in part (a) and find the least squares solution. x=
Let A1 1 and b = {12, 6, 18)T (a) Use the Gram-Schmidt process to find...
Let A1 1 and b = {12, 6, 18)T (a) Use the Gram-Schmidt process to find an orthonormal basis for the column basis for the column space of A; (b) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular; (c) Solve the least squares problem Ax = b. Use the results from problem! (c) to find the least square solution of Ax = b
(4) Suppose A = UEVT is a singular value decomposition for A. The nxm matrix At...
(4) Suppose A = UEVT is a singular value decomposition for A. The nxm matrix At = VETUT where st is defined in (1g) is called a pseudoinverse of A. Let x = Atb. (a) Show that x satisfies the equation AAx = A'b and conclude that x is a least squares solution to Ax = b. (b) Show that x = Alb lies in row(A) and conclude that x = projrow(A)(x). (c) Conclude that x is the smallest least...
Consider a matrix A є Rmxn has a full QR factorisation A = QR, with R = where Q is an orthogonal matrix and R is an upp...
Consider a matrix A є Rmxn has a full QR factorisation A = QR, with R = where Q is an orthogonal matrix and R is an upper-triangular square matrix. Consid- ering that the matrix R has an SVD R UVT, express the SVD of A in terms of Q, U, 2, and V.
Consider a matrix A є Rmxn has a full QR factorisation A = QR, with R = where Q is an orthogonal matrix and R is...
T67 [21] (1 point) Let A = 1 1 and b = [21] -6 .The QR...
T67 [21] (1 point) Let A = 1 1 and b = [21] -6 .The QR factorization of the matrix A is given by: 1-3] [21] [ 11 = [2 1 112] 2 -V2 ماده و V2 (a) Applying the QR factorization to solving the least squares problem Ax = b gives the system: (b) Use backsubstitution to solve the system in part (a) and find the least squares solution. 5/3 -3
Problem 4: (20 points) Let [ 3 -6 A= 4 -8 0 1 1) Find a...
Problem 4: (20 points) Let [ 3 -6 A= 4 -8 0 1 1) Find a QR-decomposition of A. 2) Use the QR-decomposition that you found in part 1 to find the least squares solution of the system 3 -6 4 - 8
Consider a miatrix A є Rmxn has a full QR factorisation A -QR, with R-o where Q is an orthogonal matrix and R is an upper-triangular square matrix. Consid- ering that the matrix R has an SVD R UXVT,...
Consider a miatrix A є Rmxn has a full QR factorisation A -QR, with R-o where Q is an orthogonal matrix and R is an upper-triangular square matrix. Consid- ering that the matrix R has an SVD R UXVT, express the SVD of A in terms of Q, U, 2, and V
Consider a miatrix A є Rmxn has a full QR factorisation A -QR, with R-o where Q is an orthogonal matrix and R is an upper-triangular square matrix....
Section 5.6 QR Factorization: Problem 6 Previous Problem Problem List Next Problem 2 9 (1 point)...
Section 5.6 QR Factorization: Problem 6 Previous Problem Problem List Next Problem 2 9 (1 point) Let A = 1 1 and b = 6 The QR factorization of the matrix A is given by: 2 6 1 3 1 1 -ŠV2 V2 *V2 ܝܙܚܐܝ 0 (a) Applying the QR factorization to solving the least squares problem Ax = b gives the system: 3 X= 0 3 (b) Use backsubstitution to solve the system in part (a) and find the...
7. Consider the following matrix (a) Find the QR decomposition of A using the Gram Schmidt process. (b) Use the QR decomposition from (a) to find the least-squares solution to Ax = b where -3
7. Consider the following matrix (a) Find the QR decomposition of A using the Gram Schmidt process. (b) Use the QR decomposition from (a) to find the least-squares solution to Ax = b where -3
== 2 1 3 (1 point) Let A 1 and b -3 2 6 The QR factorization of the matrix A is given by: 1 2 = ſ v2 ŠV2 0 V2 3 2 3 (a) Applying the QR factorization to solving the least squares problem Ax b gives the system: 3 wls, wie X = (b) Use backsubstitution to system in part (a) and find the least squares solution. =
2 9 11 and b (1 point) Let A -6 The QR factorization of the matrix A is given by: 2 1 6 17 äv2 3 1 1 0 3 2 3 21 V2 3 áva (a) Applying the QR factorization to solving the least squares problem Ax b gives the system: X = 0 2 3 (b) Use backsubstitution to solve the system in part (a) and find the least squares solution. x=
Let A1 1 and b = {12, 6, 18)T (a) Use the Gram-Schmidt process to find an orthonormal basis for the column basis for the column space of A; (b) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular; (c) Solve the least squares problem Ax = b. Use the results from problem! (c) to find the least square solution of Ax = b
(4) Suppose A = UEVT is a singular value decomposition for A. The nxm matrix At = VETUT where st is defined in (1g) is called a pseudoinverse of A. Let x = Atb. (a) Show that x satisfies the equation AAx = A'b and conclude that x is a least squares solution to Ax = b. (b) Show that x = Alb lies in row(A) and conclude that x = projrow(A)(x). (c) Conclude that x is the smallest least...
Consider a matrix A є Rmxn has a full QR factorisation A = QR, with R = where Q is an orthogonal matrix and R is an upper-triangular square matrix. Consid- ering that the matrix R has an SVD R UVT, express the SVD of A in terms of Q, U, 2, and V.
Consider a matrix A є Rmxn has a full QR factorisation A = QR, with R = where Q is an orthogonal matrix and R is...
T67 [21] (1 point) Let A = 1 1 and b = [21] -6 .The QR factorization of the matrix A is given by: 1-3] [21] [ 11 = [2 1 112] 2 -V2 ماده و V2 (a) Applying the QR factorization to solving the least squares problem Ax = b gives the system: (b) Use backsubstitution to solve the system in part (a) and find the least squares solution. 5/3 -3
Problem 4: (20 points) Let [ 3 -6 A= 4 -8 0 1 1) Find a QR-decomposition of A. 2) Use the QR-decomposition that you found in part 1 to find the least squares solution of the system 3 -6 4 - 8
Consider a miatrix A є Rmxn has a full QR factorisation A -QR, with R-o where Q is an orthogonal matrix and R is an upper-triangular square matrix. Consid- ering that the matrix R has an SVD R UXVT, express the SVD of A in terms of Q, U, 2, and V
Consider a miatrix A є Rmxn has a full QR factorisation A -QR, with R-o where Q is an orthogonal matrix and R is an upper-triangular square matrix....
Section 5.6 QR Factorization: Problem 6 Previous Problem Problem List Next Problem 2 9 (1 point) Let A = 1 1 and b = 6 The QR factorization of the matrix A is given by: 2 6 1 3 1 1 -ŠV2 V2 *V2 ܝܙܚܐܝ 0 (a) Applying the QR factorization to solving the least squares problem Ax = b gives the system: 3 X= 0 3 (b) Use backsubstitution to solve the system in part (a) and find the...
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