linear algebra question 0. Given 1 3-5 1 1 -2 1-3 1 and b If the Gram-Schmidt process is applied to determine an orthonormal basis for R(A), and a QR factoriza- tion of A then, after the first two or...

Question

Question

linear algebra question

0. Given 1 3-5 1 1 -2 1-3 1 and b If the Gram-Schmidt process is applied to determine an orthonormal basis for R(A), and a QR

Answer 1

Answer #1

1-35 1 12 1-3 1 (10a)Given A- 4 perfoming gram-schmidt procedure to orthogonalize, we obtain: 211 31-2 -2 2 422 4 1-3 46 31

136 1-2 1-2 1-2 1-2 | 1-2 1-2 1-2 1-2 200 200 1-2 1-2 1-2 1-2 121-2121-2 1-2 1-2 1-2 1-2 12 12 12 12 0

1 12 (10b)Given A1-3 1 and b- From QR-decompostion (a) we have 1 112 -2 -1 0 4 3 The least square solutions of the linear sys

Answer 2

Similar Homework Help Questions

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
Use the Gram-Schmidt process to find an or- thonormal basis for the subspace of R4 spanned...

Use the Gram-Schmidt process to find an or- thonormal basis for the subspace of R4 spanned by Xi = (4, 2, 2, 1)", X2 (2,0, 0, 2)", X3 = (1,1, -1, 1). Let A = (x1 X2 X3) and b = (1, 2, 3,1)7. Factor A into a product QR, where Q has an orthonormal set of column vectors and R is up- per triangular. Solve the least squares problem Ax = b.
Apply the Gram-Schmidt orthonormalization process to transform the given basis for R" into an orthonormal basis. Us...

Apply the Gram-Schmidt orthonormalization process to transform the given basis for R" into an orthonormal basis. Use the vectors in the order in which they are given. B = {(4, 1, 0), (0,0,4), (1, 1, 1)) は,ヤ) 4 .0 17 'V17 U1 Uz = | (0.0.1 ) (かか) u3 = Apply the Gram-Schmidt orthonormalization process to transform the given basis for R" into an orthonormal basis. Use the vectors in the order in which they are given. B = {(4,...

linear algebra (a) Use Gram-Schmidt, (using the given vectors as labeled) to find an orthonormal basis...

linear algebra (a) Use Gram-Schmidt, (using the given vectors as labeled) to find an orthonormal basis for the span of 0 0 V3- (b) Use Gram-Schmidt, (using the given vectors as labeled) to find an orthonormal basis for the span of 0 V3-0 v2= (c) What can we conclude from the two examples computed above? Also, did you find one computation "easier than the other? If so, what do you think made it easier?
3. Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R' spanned...

3. Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R' spanned by the vectors u; = (1,0,0,0), 12 = (1,1,0,0), uz = (0,1,1,1).
Apply the Gram-Schmidt orthonormalization process to transform the given basis for p into an orthonormal basis....

Apply the Gram-Schmidt orthonormalization process to transform the given basis for p into an orthonormal basis. Use the vectors in the order in which they are given. B = {(0, 1), (4,9)} U1 = U2 =

points PooleLinAlg4 5.3.017 1 The columns of Q were obtained by applying the Gram-Schmidt Process to the columns of A. Find the upper triangular matrix R such that A QR 2 10 6 5 A=110 10-3 , Q = Need...

points PooleLinAlg4 5.3.017 1 The columns of Q were obtained by applying the Gram-Schmidt Process to the columns of A. Find the upper triangular matrix R such that A QR 2 10 6 5 A=110 10-3 , Q = Need Help?Read It Talk to a Tutor + -1 points PooleLinAJg4 5.3.018. The columns of Q were obtained by applying the Gram-Schmidt Process to the columns of A. Find the upper triangular matrix R such that A = QR. (Enter sqrt(n)...
Use the Gram-Schmidt process to transform the basis, B = {(1,2), (3, 4)} for R² into...

Use the Gram-Schmidt process to transform the basis, B = {(1,2), (3, 4)} for R² into (a) an orthogonal basis for R and (b) an orthonormal basis for R using the Euclidean inner product; that is, dot product, and use vectors in the order in which they are given.
for the subspace of R4 consisting of 4. Use the Gram-Schmidt process to find an orthonormal...

for the subspace of R4 consisting of 4. Use the Gram-Schmidt process to find an orthonormal basis all vectors of the form ſal a + b [b+c] 5. Use the Gram-Schmidt process to find an orthonormal basis of the column space of the matrix [1-1 1 67 2 -1 3 1 A=4 1 91 [3 2 8 5 6. (a) Use the Gram-Schmidt process to find an orthonormal basis S = (P1, P2, P3) for P2, the vector space of...

Linear Algebra - Gram-Schmidt 4. (10 points) Apply the Gram-Schmidt process to the given subset S...

Linear Algebra - Gram-Schmidt 4. (10 points) Apply the Gram-Schmidt process to the given subset S to obtain an or- thogonal basis ß for span S. Then normalize the vectors in this basis to obtain an orthonormal basis ß for span S. w s={8-8-8 (b) S = { 13 -21:1-5 :7 4] [5] [11