5 3 1 0 Problem 10 Let wi = ,W2 W3 Let W = Span{W1,W2, W3} C R6. 11 9 1 2 a) [6 pts] Use the Gram-Schmit algorithm to find an orthogonal basis for W. You should explicitly show each step of your calculation. 10 -7 11 b) [5 pts) Let v = Compute the projection prw(v) of v onto the subspace W using the 5 orthogonal basis in a). c) (4 pts] Use the computation in b) to...
7. Let W = Span{x1, x2}, where x1 = [1 2 4]" and X2 – [5 5 5]" a. (4 pts) Construct an orthogonal basis {V1, V2} for W. b. (4 pts) Compute the orthogonal projection of y = [0 1]' onto W. C. (2 pts) Write a vector V3 such that {V1, V2, V3} is an orthogonal basis for R", where vi and v2 are the vectors computed in (a).
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto C(A) with its error vector. b) Find the least squares approximation, £, to the solution vector x of Ai- c) The least squares error is defined to be the length of the vector b - AX. Find this vector and its length. d) What is the relationship between A, , and p? 4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto...
0.5 -0.5 0.5 (1 point) Let A = -0.5 Note that the columns of A are orthonormal (why?). 0.5 0.5 0.5 0.5 -1 -2 (a) Solve the least squares problem Ax = b where b - -2 0 (b) Find the projection matrix P that projects vectors in R4 onto R(A) P = (c) Compute Ax and Pb Pb = 0.5 -0.5 0.5 (1 point) Let A = -0.5 Note that the columns of A are orthonormal (why?). 0.5 0.5...
2 2 2 Let y = 6,41 . - uz = کہانی and W = Span {uq,42}. Complete parts (a) and (b). 1 WN w UTUS a. Let U = = [u un uz]. compute UTU and UU! and UUTA (Simplify your answers.) b. Compute projwy and (UT)y. projwy = and (uu)y=(Simplify your answers.)
Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax=b. 0 1 -11 10-11 1 1 1 A / b = - 1 1 0 a. The orthogonal projection of b onto Col A is b = (Simplify your answers.) b. A least-squares solution of Ax = b is = 1 (Simplify your answers.)
Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax = b. 0 1 -1 1 1 0 - 1 3 A= , b= 1 1 5 -1 1 0 7 a. The orthogonal projection of b onto Col A is = (Simplify your answers.) b. A least-squares solution of Ax = b is x= (Simplify your answers.)
Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax b. 8 1 -7 1 b- 1-17 a. The orthogonal projection of b onto Col A is b-(Simplify your answer) (Simplify your answer.) b A least-squares solution of Ax-b is x Find (a) the orthogonal projection of b onto Col A and (b) a least-squares solution of Ax b. 8 1 -7 1 b- 1-17 a. The orthogonal projection of b onto Col...
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...
Question 1 2 pts Describe the span of {(1,0,0),(0,0,1)} in R3 The x-z plane R3 R2 The x-y plane Question 2 2 pts Describe the span of {(1,1,1),(-1,-1, -1), (2,2, 2)} in R3 A plane passing through the origin Aline passing through the origin R3 A plane not passing through the origin A line not passing through the origin Question 3 2 pts Let u and v be vectors in R™ Then U-v=v.u True False Question 4 2 pts Ifu.v...