2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α 0 and for every 0 < i k one has that α, κ α, > , αϊ-1 3. Find a l...
3. Consider the following vectors, where k is some real number. H-11 Lol 1-1 a. For what values of k are the vectors linearly independent? b. For what values of k are the vectors linearly dependent? c. What is the angle (in degrees) between u and v? 4. Here are two vectors in R". Let V = the span of {"v1r2} a. Find an orthogonal basis for V (the orthogonal complement of V). b. Find a vector that is neither...
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
1. Determine whether or not the four vectors listed above are linearly independent or linearly dependent. If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) Otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds. (1 point) 13--3-3 Let vi = and V4 1-11 Linearly Dependent 1. Determine whether or not the four vectors listed above are linearly independent...
prove (3) 233 Theorem. (1) If 31,23,. iTn are linearly independent vectors in X then there are TA -İ, in X" such, that' A(x)=6',ond (2) If X is infinite dimensional then so is X 3) Every finite dimensional vector subspace of X has a complement. (4) If Y is a finite dimensional vector subspace of X then Y = ran P for some bounde idempotent linear map P:X X Prof. (1) Let := span xi. Then Y, is a closed...
1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1, 2+2-2,1 +32"} b. {2+1, 3x +3',-6 +2"} 8. Let T be a linear transformation from a vector space V to W over R. . Let .. . be linearly independent vectors of V. Prove that if T is one to one, prove that (un)....(...) are linearly independent. (m) is ) be a spanning set of V. Prove that it is onto, then Tu... h...
(1 point) Suppose S = {r, u, d} is a set of linearly independent vectors. If x = 4r + 2u + 5d, determine whether T = {r, u, 2} is a linearly independent set. Select an Answer 1. Is T linearly independent or dependent? IfT is dependent, enter a non-trivial linear relation below. Otherwise, enter O's for the coefficients. u+ !!! I=0
(a) Determine whether the following vectors are linearly independent: 1 subpts (b) Find Span{v1, V2, V3}. 1 subpts
1) a)Find the rank of A. b) Are the following vectors linearly independent? ſo 1 27 [2] [1] [0] A = 2 0 5 u = 5 uz = 0 uz = 2 0 0 0 To o o 2) What are the eigenvalues and the spectral radius of (4 0 27 B= 0 2 0 Bonus: Find one of the eigenvectors of B. 001
6. Given the vectors vi = - 0 -- --(2.).-) no estaba 1. vz = 2 .03 = 1 -1 1 62-5) ,0 = 3, find the value(s) of k so that: de (a) vis in Span{vi, v2, U3}. (b){i, 03, 03} form a linearly independent set. (c){vi, už, va} form a basis for R3. (d) span{ti, uz, va} is a plane in R.
(1 point) Find a linearly independent set of vectors that spans the same subspace of R3 as that spanne -3 3 3 2 -5 -2 4 0 Linearly independent set: