Let W = span L-210cans 1%, Construct an orthonormal basis for W. Llo) Onlin
Let W Span((2,-3,0, 1), (4,-6,-2, 1), (6,-9,-2,2) R4. (a) Find a basis for W (b) Find a basis for W (c) Find an orthogonal basis for W and W (d) The union of these two orthogonal bases (put the basis for W and W what? Why is the union orthogonal? into one set) is an orthogonal basis for Let W Span((2,-3,0, 1), (4,-6,-2, 1), (6,-9,-2,2) R4. (a) Find a basis for W (b) Find a basis for W (c) Find...
Let W = span{.x2, 2x + x2,1+2x+x2} in P2. Use Gram-Schmidt to find an orthogonal basis for W. Use the standard inner product for P2, do + a1x + a222, bo + b1X + b222 = aobo +ajbı + a2b2.
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).
20 3. Let 1 = 2 and = 5. Let W = Span{11, 13). (a) Give a geometric description of W. (b) Use the Gram-Schmidt process to find an orthogonal basis for W. (c) Let = 2 Find the closest point to į in W. (a) Use your orthogonal basis in part (b) to find an orthonormal basis for W.
e, none of these 7. Let {1,..., up} be an orthogonal basis for a subspace W of R" and {...., } be an orthogonal basis for Wt. Determine which of the following is false. a. p+q=n b. {U1,..., Up, V1,...,0} is an orthogonal basis for R". c. the orthogonal projection of the u; onto W is 0. d. the orthogonal projection of the vi onto W is 0. e. none of these 8. Let {u},..., up} be an orthogonal basis...
2. Let M,, be equipped with the standard inner product. Prove. u is orthogonal W-span w,w,w) 3 -1 note: You must use some of the axioms in the definition of an inner product 2. Let M,, be equipped with the standard inner product. Prove. u is orthogonal W-span w,w,w) 3 -1 note: You must use some of the axioms in the definition of an inner product
Let W = span{ (-2, 1; 2,0), (4,0-5, 2)] the Groun - Student Produrt to find an enthonormal basis for W The dimension of wt, the orthogonal complement of w.is basis from (a), either before or after normalizing projw (1,1,1,). be your to find
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...
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.