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5. (5 pts) Explain why the vectors ū=(4,2) and 7 =(-1,6) are linearly independent (the best...
(10 points) Are the vectors ū linearly dependent [25 1], ū = [-5 -5 o] and ū = [-5 -3 2] linearly independent? If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation below true. ũ+ ö+ ū = 0.
To 17. Determine whether the vectors f(1,2,3), (1,-1,2), (1,-4,2)) in R3 are linearly independent.
Exercise 2 : 10 pts (5pts each) 1. Determine if the following vectors are linearly independent vii. Using the definition (i.e. kıvı+k_202 + .. + kūri = 7) viii. Using a determinant a. ū = (-1,2) and = (0,1) b. ü =(3,-6) and 3 = (-4,8) c. ū= (1,2), v = (3,1) and w = (2-2) d. i = (1,4,-3), i = (0,7,1) and w = (0,0,1) e. ü= (-1,2,0), v = (4,1, -3) and w = (10.-2.-6) f. ū=...
1. Determine (by inspection) why the vectors below can or cannot be linearly independent. Explain your answer. [ 31 rol [6] (a) 5 1,0 5 [-1] [ 0 ] [ 4 (b) | | [3][] 2 -11 L aan RS then
1. We are given the following vectors: ū = (x,0,4), ū = (2,1,1) a) What does the value of x need to be so that the vectors ū and ū are perpendicular? Explain your reasoning. (5 pts.) b) Calculate the cross product p = ū xū and find the magnitude of p. (5 pts.) c) Calculate the cross product q = ū xū and find the magnitude of q: (5 pts.) d) Compare the magnitude of p with the magnitude...
= 5. Determine if the following are linearly independent subsets: a) Determine whether or not vectors (1,-1,1,1), (3,0,1,1), (7,-1,2,1) form a linearly independent subset of R4. [1 01 To 27 -2 1] Let A= and C = . Do A, B, and C form 2 -1 -1 1 a linearly independent subset of M2x2? c) Determine if 5,x? – 6x,(3 – x)² form a linearly independent subset of F(-00,00). 6. Are the following bases? Why or why not. a) {(1,0,2),...
4 (1 point) Are the vectors -5 H4 0 and -20 linearly independent? 3 linearly independent If they are linearly dependent, enter a non-trivial solution to the equation below. If they are linearly independent, enter the unique solution to the equation below. 4 -5 + 0 0
4 Q1. Consider the following set of vectors3,0 4 (a) Show that these vectors are linearly independent. (b) Do these vectors span a plane? Explain your answer. (c) Is the set a basis for R5? Why, or why not? 4 Q1. Consider the following set of vectors3,0 4 (a) Show that these vectors are linearly independent. (b) Do these vectors span a plane? Explain your answer. (c) Is the set a basis for R5? Why, or why not?
my solutions say linearly independent but i dont understand why 4. (5 pts) Let zu(e) = (2-1), sz(t) = [et] Determine whether the vector functions are linearly dependent or linearly independent on (-0,00). ww/xix.7(4) = fet to +-+-0 W[X, Xz] (t) = 0
3. Which of the following set of vectors in R3 are linearly independent Explain your answer.