#9 6.3.17 2 3 win win Let y = 8,0 = = and W = Span (41,42}. Complete parts (a) and (b). 2 3 1 3 a. Let U 41 42 2]. Compute U'U and Uu? UTU- and UUT - (Simplify your answers.)
انسانية نان Let y=1 داني ? and W = Span 4u,uz. Complete parts (a) and (b). ماني داني د a. Let u= [ u, uz]. Compute UỮU and UU? 0 0 = and U0T = (Simplify your answers.)
Find the best approximation to z by vectors of the form C7 V + c2V2. 3 1 3 -1 -6 1 z = V2 4 0 -3 3 1 The best approximation to z is . (Simplify your answer.) - 15 - 8 8 - 1 Let y = , and v2 Find the distance from y to the subspace W of R* spanned by V, and vą, given 1 0 1 - 15 3 3 - 13 09 that...
Verify that (u,,uz) is an orthogonal set, and then find the orthogonal projection of y onto Span (u.uz). 1-17 [3] 2,,= -1 . uz = = To verify that (uy,uz) is an orthogonal set, find u. U. Uyuz = 0 (Simplify your answer.) The projection of y onto Span{u,, 42} is (Simplify your answers.)
Verify that (41.uz) is an orthogonal set, and then find the orthogonal projection of y onto Span{41.42}- y = 1 0 To verify that {0, 42} is an orthogonal set, find u, '42. u U2 - 0 (Simplify your answer) The projection of y onto Span{u, uz} is (Simplify your answers)
Wite **the sum of two vectons, one in Span {u) and one in Span (wa). Assume that (.....) is an orthogonal besis Type an integer or simplified traction for each max element) Verity that {.uz) is an orthogonal sot, and then find the orthogonal projection of y onto Span(uz) y To verty that (0-uz) as an orthogonal set, find u, uz 2-0 (Simplify your answer.) The projection of yonte Span (0,2) 0 (Simplify your answers.) LetW be the subspace spanned...
Verify that {u7,42} is an orthogonal set, and then find the orthogonal projection of y onto Span{uq, 42}- 6 3 - 4 y- . 01 u:- -2 0 To verify that (14,42} is an orthogonal set, find uy • 42. u uy - (Simplify your answer.) The projection of y onto Span{44,42} is .. (Simplify your answers.)
#5 6.3.8 Let W be the subspace spanned by U, and up. Write y as the sum of a vector in W and a vector orthogonal to W. -1 -2 y = un = 3 2 -1 The sum is y = y +z, where y 8. is in W and z = Doo is orthogonal to W. (Simplify your answers.)
Let W be the subspace spanned by u, and up. Write y as the sum of a vector in W and a vector orthogonal to W. 2 y = 6 un 5 The sum is y=9+z, where y is in W and Z is orthogonal to W. (Simplify your answers.) N
Question 5 pts 2 1 -1 0 Span{ Let W = }. 1 1 -1 0 1 (a) Compute the othogonal projection of onto W. 1 Write your solution here 2 1 -1 0 1 and b = (b) Find the least squares solution to Ax = b, for A = 1 1 1 -1 1 0 0 0 1 Write your solution here (c) Explain the relationship between your answers for the first two parts of the question. Write...