(i) Suppose L = {(1, 4, 2, 2),(2, 2, 1, 2),(2, 4, 2, 1)}. Is L linearly independent in R^4 ? Justify your answer.
(ii) Suppose S = { 0 0 1 0 , 0 2 3 0 , 4 1 0 0 }. Is S linearly independent in M2(R)? Is span(S) = M2(R)? Justfy your answers.
(i) Suppose L = {(1, 4, 2, 2),(2, 2, 1, 2),(2, 4, 2, 1)}. Is L linearly independent in R^4 ? Just...
(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
2. (a) Is the collection 1 2 linearly dependent or linearly independent? Justify. [2 (b)Describe (geometrically) the following span as lines, planes or all of R3 2 Span〉 | 2 -3
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 linear system with real coefficients for which the span of
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...
Without calculation, find one eigenvalue and two linearly independent eigenvectors of A2 2 2 Justify your answer One eigenvalue of A is0 because the columns of A are linearly dependent. Two linearly independent eigenvectors of A arebecause (Use a comma to separate answers as needed.)
Without calculation, find one eigenvalue and two linearly independent eigenvectors of A2 2 2 Justify your answer One eigenvalue of A is0 because the columns of A are linearly dependent. Two linearly independent eigenvectors of...
2 2 2 Without calculation, find one eigenvalue and two linearly independent eigenvectors of A= Justify your answer. 2 2 2 2 2 2 One eigenvalue of A is 0 because the columns of A are linearly dependent. 1 because the entries of each vector are equal. Two linearly independent eigenvectors of A are -1 2 (Use a comma separate answers as needed.)
747-38 1026 59% webwork.math.mcgill.ca Problem 5 linearly dependent linearly dependent At least one of the answers above is NOT correct. 15 o to O- 40 (1 point) Let Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 15 B = 12 1-6 -9 -4 3 -101 -8 4 ] (a) Find the reduced row echelon form of the matrix B mref(B) = (b) How many...
1. (16 points) Determine whether the given set of functions is linearly dependent or linearly independent on the indicated interval. Justify your answers. (a) (8 points) S(x) = x + 2cos?x, S2(x) = 3 sin’x, S(x) = x + 2 on (0,0). (b) (8 points) (x) = and f(x) = differential equation " + 1" 4x are solutions of the linear homogeneous O on () 12
ǐ Question He. Determine whether the given functions are linearly dependent or linearly independent on the specified interval Justify your decision Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The functions are Iinearly dependent because for constant values,e, and cy, the equation cye S .r has the solution c, and c O B. The functions are linearly independent beceuse there are no constant values,e, and eg, that make the...
Please solve using matrices and not equations.
Thanks.
2. Given the columns of the matrix u v w 0 1 2 0-1 0 0 r S t -1 021 01 0 For each of the sets of vectors given below, answer the following questions: (i) Is the set linearly independent? 1 Does the set span (iii Does the vector a- (a) S (r, s, t, u) (b) T fr,t, 0, u) (c) U = {r, t, w, u, v} (3,2,1,5)...
Determine whether the set S is linearly independent or linearly dependent. 2 -4 S={ 3 2 Note: you can only submit each part of this question once for marking. 2 -4 STEP 1: Determine if is a scalar multiple of 3 2 O scalar multiple O not a scalar multiple STEP 2: Determine if the set S is linearly dependent. O linearly independent linearly dependent