6. Let R* be equipped with the dot product and let B = {(1,-1,1),(1,0,1),(1,1,2)). B is...
4. Let R3 be equipped with the dot product and let B = {(2,1,1),(0,4,-2),(3,5, -1)}. B is a basis for R?. Use the Gram-Schmidt process to convert B into an orthonormal basis.
4. Let R3 be equipped with the dot product and let B = {(2,1,1),(0,4,-2),(3,5, -1)}. Bis a basis for R3. Use the Gram-Schmidt process to convert B into an orthonormal basis.
4. Let R3 be equipped with the dot product and let B = {(2,1,1),(0,4,-2),(3,5, -1)}. B is a basis for Rs. Use the Gram-Schmidt process to convert B into an orthonormal basis.
NEED (B) AND (C) 2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space C(I-1,1) of continuous real-valued funo- tions on the domain [-1, 1] (b) Use the Gram-Schmidt process to find an orthonormal basis for P2(R) with re- spect to this inner product (c) Find a polynomial q(x) such that for every p E P2R 2. (a) Prove that 1 (f, g)=| x2 f(x)g(x)dx is an inner product on the vector space...
Use the Gram-Schmidt process to transform the basis, B = {(1,2), (3, 4)} for R² into (a) an orthogonal basis for R and (b) an orthonormal basis for R using the Euclidean inner product; that is, dot product, and use vectors in the order in which they are given.
Let A1 1 and b = {12, 6, 18)T (a) Use the Gram-Schmidt process to find an orthonormal basis for the column basis for the column space of A; (b) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular; (c) Solve the least squares problem Ax = b. Use the results from problem! (c) to find the least square solution of Ax = b
Let uj = [1,1,1]* and u2 = [1,2,2]t be vectors in R3 and V be the vector space spanned by {u1, U2}. a. 6pt Use Gram-Schmidt orthogonalization to find an orthonormal basis for V. b. 4pt Let w = [1,0,1)+. Find the vector in V that is closest to w.
6. Let P be the subspace in R 3 defined by the plane x − 2y + z = 0. (a) [5 points] Use the Gram–Schmidt process to find orthogonal vectors that form a basis for P. (b) [5 points] Find the projection p of b = (3, −6, 9) onto P. 6. Let P be the subspace in R3 defined by the plan 2y+z0 (a) [5 points] Use the Gram-Schmidt process to find orthogonal vectors that form a basis...
Question 3. Let 3 5/' and for x(2),y -(,) ER2 define (a) Show that the assignment (x, y) > (x,y) defined ın (1) us an nner product [10 marks (b) If a - (1,-1) and b - (1,1), then show that the vectors a and b are lınearly ndependent but they are not orthogonal with respect to the inner product n (1) 3 marks] (c) Given the vectors a and b in (b), the set (a, by is hence a...
a) Verify that B is a basis for IR3 (b) Use the Gram-Schmidt process to produce an orthogonal basis for R (c) Normalize the vectors to produce an orthonormal basis for R3.