(1 point) Let c=1 ). 6 = [-), = [E]. * = [1] Is ū a linear combination of the vectors ū1, ū2 and ū3 ? choose If possible, write ū as a linear combination of the vectors ū1, 72 and 73. For example, the answer ū = 4ū1 + 5ū2 + 6Ū3 would be entered 4v1 + 5v2 + 6v3. If ū cannot be written as a linear combination of the vectors ū1, 72 and 73, enter DNE. ū...
1. Show that {ū1, ū2, ū3} is an orthogonal basis for R3, and write ž as a linear combination of the vectors {ū1, ū2, ū3}, 1 ū1 -[:] -2 -2 ū2 = [ ] ū3 = Ž -11 -3 -17
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...
-12 -4 8. (4 pts) Let ū1 = -12 and U2 = -15 These vectors form a basis for a subspace -6 -11 V of R3. Starting with 71, 72, use the Gram-Schmidt process to find an orthonormal basis ū1, ū2 for V. -
1. [10] Let CONH V1 = 1 , V2 = and ū3 = 1 __ Find, with justification, a vector ✓A E R4 for which {ū1, V2, V3, VA} is a basis of R4.
Show that the set of vectors {ū1 = (1,1,1,1), Ū2 = (1,0,-1,0), Ūz = (0,1,0, -1)} is orthogonal. Use those vectors in the set to get an orthonormal set {1, W2, W3}.
Let W = Span{ū1, ū2}. Write y as the sum of a vector We W and a vector zew, 1 0 -2 17 -11 3 ū1 = 2 y= 2 0 2
(1 point) Let A 0.5 -0.5 0.5 -0.5 0.5 0.5 0.5 0.5 Note that the columns of A are orthonormal (why?). 3 2 (a) Solve the least squares problem Ax b where b 3 <X = (b) Find the projection matrix P that projects vectors in R* onto R(A) P (c) Compute Aî and Pb A Pb
0.5 -0.5 0.5 -0.5 (1 point) Let A = . Note that the 0.5 0.5 0.5 0.5 columns of A are orthonormal (why?). (a) Solve the least squares problem Ax = b where b = Il (b) Find the projection matrix P that projects vectors in Ronto R(A) P= (c) Compute Ax and Pb Ax= Pb =
Latin = and l [1 + 3i -2i (a) Verify that ởi and ū2 are orthogonal. (b) Let S = Span{ū1, ū2} and ū= الد ) - 3 3 + 2i . Find projgū.