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 bo...
#7
6.3.13 Find the best approximation to z by vectors of the form C1V4 +C2V2 2 3 1 -6 - 1 2 za VE V2 3 -3 0 2 1 1 The best approximation to z is (Simplify your answer.)
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 3 13 The vectors V1 = | 2 and V2 = 5 span a subspace V of the indicated Euclidean space. Find a basis for the orthogonal complement vt of V. 8 36 4 13 Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. O A. A basis for the orthogonal complement vt is {}. (Use a comma to separate vectors as needed.) OB. There is no basis for the orthogonal...
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...
15 points) Consider the following vectors in R3 0 0 2 V1 = 1 ; V2 = 3 ; V3 = 1] ; V4 = -1;V5 = 4 1 2 3 = a) Are V1, V2, V3, V4, V5 linearly independent? Explain. b) Let H (V1, V2, V3, V4, V5) be a 3 x 5 matrix, find (i) a basis of N(H) (ii) a basis of R(H) (iii) a basis of C(H) (iv) the rank of H (v) the nullity...
Start Typing in MATLAB Use MATLAB: 1.) Determine if the vectors V1 = (2,-1,2,3), V2 = (1,2,5, -1), V3 = (7,-1,5,8) form a basis for R4. Type: BA1 = [2 – 1 2 3;1 2 5 – 1;7 -15 8]' BAR1 = rref(BA) If you decide that V1, V2, V3 form a basis for R, type: ANBA1= 1 Otherwise type: ANBA1=0 2.) Determine if the vectors V1 = (1,2,3), V2 = (2,9,0), V3 = (3,3,4) form a basis for Rº....
#8
6.4.8 Question Help 1 The vectors v1 1 -2 and V2 form an The orthonormal basis of the subspace spanned by the vectors is O. (Use a comma to separate vectors as needed.) 5 3 orthogonal basis for W. Find an orthonormal basis for W.
1. a) Calculate the angle between the vectors V1 = (2, 3,-4) and v2 =(-3, 4, 2) b) Are the vectors P1 = (2, 4, -3) and p2 = (4, 1, 4) orthogonal? Why or why not? c) What is the distance between pı and pz? d) Calculate the cross product, pe X P2.
Linear Algebra
6. (8pt) (a) Find a subset of the vectors v1 = (1, -1,5,2), V2 = (-2,3,1,0), V3 =(4,-5, 9,4), V4 = (0,4,2, -3) V5 = (-7, 18, 2, -8) that forms a basis for the space spanned by these vectors. (b) Use (a) to express each vector not in the basis as a linear combination of the basis vectors. (c) Let Vi V2 A= V3 V4 Use (a) to find the dimension of row(A), col(A), null(A), and of...
- 4 -1 -2 1 Let y = V1 = and V2 Find the distance from y to the subspace W of R4 spanned by V, and V2, given that the closest 1 -1 0 13 3 -1 -5 point to y in W is y= نيا 9 The distance is (Simplify your answer. Type an exact answer, using radicals as needed.)