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 orthonormal vectors qi and q are computed, we have 2 -2 2 2 2 2 2 (a) Finish the process. Determine q3 and fill in the third columns of Q and R (b) Use the QR factorization to find the least...
Let V1 = (1,2,0)^T, V2 = (2,4,2)^T, and V3 = (0,2,7)T and A = [V1,V2,V3] 5) (20 points) Let vi = (1,2,0)T, v2 = (2,4, 2)T and v3 = (0, 2.7)T and A- [v1, v2, v3 a) Find an orthonormal basis for the Col(A) b) Find a QR factorization of A. c) Show that A is symmetric and find the quadratic form whose standard matrix is A
== 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=
for the question, thanks for your help! 2. Let 2 -2 -11 1 3 S1 8 and b -2 -5 7 A= -4 5 2-9 18 Moreover, let A be the 4 x 3 matrix consisting of columns in S (a) (2.5 pt) Find an orthonormal basis for span(S). Also find the projection of b onto span(S) (b) (1.5 pt) Find the QR-decomposition of A. (c) (1 pt) Find the least square solution & such that |A - bl2 is...
#15 6.4.25 Question Help - 10 -4 5 8 - 10 3 6 0 2 2 8 5 12 - 6 - 12 30 , is 3 -3 4 o . Find the QR factorization of A An orthogonal basis for A, -6 6 16 16 28 28 16 0 0 8 5 4 2 3 0 -4 2 with the given orthogonal basis. The QR factorization of Ais A = QR, where Q= and R =
5 1 -2 0-4 Let A=0 0 0 0 13 1 -2 0 -3 5 a. Find a basis for Col A and find Rank A. b. Find a basis for Nul A.
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
1 2 0 1 10. Let A = 2 3 1 1 3 5 1 2 (a). Find the reduced row echelon form of A. (b). Using the answer for (a), find rank(A), and find a basis for Col(A). (c). Using the answer for (a), find a basis for Nul(A).
3 0 6 (a) Let x1 = 2 X2= and write W = span{X1, X2} 21 Find X1 X2 and enter your answer in the box below. X1 X2 = Number We then apply Gram-Schmidt to find an orthonormal basis for W. V1 = X1 v2 = x2 - projv112 Find V2 and enter your answer in the box below. We then normalise the basis {V1, V2} to form an orthonormal basis {01, 12} (0) in Maple syntax, should be...