
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.)
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...
a. Let U = [ u1 u2]. Compute UTU and
UUT
b. Compute projwy and (UUT)y
65 2 2 2 481 e.
65 2 2 2 481 e.
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...
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...
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)
Let V = M2(R), and let U be the span of
S =
2. (a) Let V = M,(R), and let U be the span of s={(1 1) ($ 3). (3), (1 9). (1) 2.)} Find a basis for U contained in S. (b) Let W be the subspace of P spanned by T = {2} + 22 – 1, -2.3 + 2x +1,23 +22² + 2x – 1, 2x3 + x2 +1 -2, 4.23 + 2x2 - -4}. Find...
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
3 - 2 Let u= Note that {u, v, w} is an orthogonal set of vectors and w - -3 4 9 be a vector in subspace W, where W = Span{u, v, w}. Let y= 11 -27 Write y as a linear combination of u, v, and uw, i.e. y = ciu + cqũ + c3W. Answer: y=