1. (4 marks) Show that the set of vectors {7: = (1,1,1,1), 7x = (1,0,−1,0), 7:...
1. (4 marks) Show that the set of vectors {ős = (1,1,1,1), in = (1,0, -1,0), öz = (0,1,0, -1)} is orthogonal. Use those vectors in the set to get an orthonormal set {wi, wz, ws}.
Show that the set of vectors {ū1 = (1,1,1,1), Ū2 = (1,0,-1,0), Ūz = (0,1,0, -1)} is orthogonal. Use those vectors in the set to get an orthonormal set {1, W2, W3}.
LINEAR ALGEBRA 1. (4 marks) Show that the set of vectors {ū = (1,1,1,1), űz = (1,0, -1,0), vz = (0,1,0, -1)} is orthogonal. Use those vectors in the set to get an orthonormal set {w1, W2, W3}.
2. (6 marks) Find the best line y = c+dt to fit y = 1, 1, 2, 2 at times t = -1, 0, 1, 2. (Use the least squares approximation.)
LINEAR ALGEBRA 2. (6 marks) Find the best line y=c+dt to fit y=1, 1, 2, 2 at times t=-1, 0, 1, 2. (Use the least squares approximation.)
Find the best line y = c+dt to fit y = 1, 1, 2, 2 at times t=-1, 0, 1, 2. (Use the least squares approximation.) 9
(a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal projection of the vector (1,-3) on the vector v- (-1,5). 2 marks] (c) Using your result for part (b) verify that w = u-prolvu is perpendicular to V. 2 marks] (a) Write the vector aas a linear combination of the set of orthonormal basis vectors 2 marks] (b) Find the orthogonal projection of the vector (1,-3) on the vector...
The set of vectors {x1, x2} spans a subspace W of R’, where x1 = 4 2 5 and x2 ܕ ܩ ܟ 6 -7 (a) Use the Gram-Schmidt process to find an orthogonal basis for W. (b) Then normalize this new basis, so that it is an orthonormal basis. (c) Once you've found an orthonormal basis, demonstrate that it is indeed orthogonal after normalization. (d) For a bonus 2 points, calculate a third vector orthogonal to your basis and...
The set of vectors {x1, x2} spans a subspace W of R’, where x1 = 4 2 5 and x2 ܕ ܩ ܟ 6 -7 (a) Use the Gram-Schmidt process to find an orthogonal basis for W. (b) Then normalize this new basis, so that it is an orthonormal basis. (c) Once you've found an orthonormal basis, demonstrate that it is indeed orthogonal after normalization. (d) For a bonus 2 points, calculate a third vector orthogonal to your basis and...
5. For parts (a)-(d) below, consider the set of vectors B = {(1,2), (2, -1)}. (a) (2 points) Demonstrate that B is an orthogonal set in the Euclidean inner product space R2. (b) (3 points) Use the set B to create an orthonormal basis in the Euclidean inner product space R2 (e) (7 points) Find the transition matrix from the standard basis S = {(1,0),(0,1)} for R2 to the basis B. Show all steps in your calculation. (d) (7 points)...