#7 6.3.13 Find the best approximation to z by vectors of the form C1V4 +C2V2 2...
Find the best approximation to z by vectors of the form CV + C2V2 4 The best approximation to zis (Simplify your answer.)
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...
Find the best approximation to z by vectors of the form civic2V2 1 1 -5 -4 -5 1 V1 V2 -2 4 0 -2 5 2 You must fill in both of the boxes below before submitting. Give exact answers, using integers, fractions or exactly equivalent decimals. You may use a calculator for the arithmetic operations. 3/35 -13/30 Ci = C2 = Find the best approximation to z by vectors of the form civic2V2 1 1 -5 -4 -5 1...
Compute the error of each approximation, and then determine which form fits the data the best 3. (20 pts) Consider the nonlinear system 6x1 2 cos(3)-1-0 9r2 + Vr| + sin(za) + 1.06 + 0.9 = 0, Solve this system by i) Newton's method, (ii) Broyden's method. For both methods, use the initial approximation x() = [0,0,0], and the stopping criteria llx(k) X(k 1) I < tol = 10-9. Here 1-1 is the Euclidian 2-norm Display the results for each...
Consider the following three vectors in ; v1 = (1, 7, −2), v2 = (4, 3, 5), v3 = (2, −11, 9): i) Say whether v1, v2, v3 are linearly dependent or linearly independent. (Justify) ii) Say if v1, v2, v3 generate . (justify) iii) If it exists, determine the constants c1, c2, c3, such that c1v1 + c2v2 + c3v3 = (0, −5, 13/5), or argue why it cannot be written as a linear combination. We were unable to...
1. (4 marks) Show that the set of vectors {7: = (1,1,1,1), 7x = (1,0,−1,0), 7: = (0,1,0, -1)} is orthogonal. Use those vectors in the set to get an orthonormal set {to, to, s}. 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.)
7. Prove that the function N4-i/z is conformal in its entire domain Ω-C\ {0}. Find the image wo of the point v3 i under this function, as well as the rotation angle and the stretching/contracting factor of tangent vectors at this point. Find the images Vi and V2 of the vectors vi-1-(1,0) and v2 (0,1) under this map, and check that the angle between the images is the same as the angle between vi and v2 7. Prove that the...
3 3 -16 -2 -5 12 4 1-12 Find the reduced row echelon form of the matrix B 0 0 0 0 0 0 -16 12 -5 1, and v3 = 1-12 Let Vi 4 17 5 Decide whether the following statements are true or false. 2 The vectors vi, V2, and v span R. The vectors vi , V2 , and V3 are linearly independent. 3 3-16 В 1-2-5 4 -1 -12 Find the reduced row echelon form of...
Find sine bex tan = v2 3 cos > 0 7 2 sin = (Simplify your answer, including any radicals. Use integers or fractio Enter your answer in the answer box. < Previoun