(1 point) Suppose V1, V2, U3 is an orthogonal set of vectors in R. Let w...
חו (1 point) Suppose V1, V2, V3 is an orthogonal set of vectors in R Let w be a vector in span(V1, V2, V3) such that (v1,vi) = 24, (v2,v2) = 21, (V3, V3) = 9, (w,v) 120, (w, v2) = 147, (w,v3) -36, Vi+ V2+ then w= V3.
Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in span(V1, V2, V3) such that (V1, V1) = 51, (V2, V2) = 638, (V3, V3) = 36, (w, V1) = 153, (w, v2) = 4466, (w, V3) = -36, then W = _______ V1 + _______ V2+ _______ V3.
(1 point) Let {uj, u2, u2 ) be an orthonormal basis for an inner product space V. Suppose y = qui + buz + cuz is so that|lvl1 = V116. (v, uz) = 10, and (v. uz) = 4. Find the possible values for a, b, and c. a = CE (1 point) Suppose U1, U2, Uz is an orthogonal set of vectors in Rº. Let w be a vector in Span(v1, 02, 03) such that UjUi = 42, 02.02...
I am looking for how to explain #4 part b. I have gotten the matrix A and I believe the answer is W = span{ v1 u2 u3 } however I'm not really sure if that is correct or not. Please give a small explanation. Also im not sure if I need to represent the vectors in A as columns or rows, or if either one works. For the next two problems, W is the subspace of R4 given by...
Please show the detail, thank you! (1 point) (a) Let -4 -7 -2 -4 V1 = and V2 = 1 6 0 2 and let W = span{V1, V2}. Apply the Gram-Schmidt procedure to vi and V2 to find an orthogonal basis {uj, u2 } for W. uj = U2 = -13 2 (b) Consider the vector v = - Find V' E W such that || V – v' || is as small as possible. 15 8 V =...
V1 = 1 , V2= -1 , U3 = , 04 = 1 , 05 = 6 -3 0 | 2 Let S CR5 be defined by S = span(01, 02, 03, 04, 05). A. Find a basis for S. What is the dimension of S? B. For each of the vectors 01, 02, 03, 04, 05 which is not in the basis, express that vector as linear combination of the basis vectors. C. Consider the vectors W1 = 14,...
suppose that s=(v1,v2,......vm) is a finite set of linearly independent vectors in V, and w ∈ V some other vector. Let T= S ∪ (W). Prove that T is not linearly independent if and only if w∈ span(s).
= (5,7,3)}. Does the vector (1,2,0), v2 (2, 1,3), v3 15 p. #4 Consider the set of vectors in R, S= {v w(3,-1,2) belong to the Span{v1, U2, U3)? Justify your answer!
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).
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...