Determine if the given set of vectors is linearly independent or linearly dependent. (a) (4 points)...
Determine whether the given set of vectors is linearly dependent or linearly independent. U1 = (1, 2, 3), u2 = (1, 0, 1), uz = (1, -1, 5) linear dependent linear independent
*) . Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them of the form C. Cz, and C as real numbers. If the vectors are linearly independent, enter INDEPENDENT.) *(). *--(). *»( (C1,C2,C)-
Determine if the set of vectors spans R. (a) (4 points) (19.10.12 Circle one. (spans or does not span) Explain your reasoning in one sentence. (b) (4 points) 9 6 3 Circle one. (spans or does not span) Explain your reasoning in one sentence.
Determine whether the given sets of vectors are linearly dependent on mearly independent. Be sure to explain your work 21 0 0 0 54 3 2 1
Q3. Determine whether the set of vectors in P2 is linearly dependent or linearly independent. S= {2 - x, 4x – x², 6-7x + x>). Q4. Show that the following set is a basis of R. --00:07)}
(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) fi(x) = x + 2cos²x, f(x) = 3sin’x, f(x) = x + 2 on (-0,co). (b) (8 points) fi(x) = e34 and 12(x) = e 4x are solutions of the linear homogeneous differential equation y" + y' - 12y = 0 on (-0,co).
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
Determine whether the members of the given set of vectors are linearly independent. Show all work. If they are linearly dependent, find a linear relation among them. a) --0----0 --0 b) 2 *(1) = 0-0 =
WURG Will Calculations: 4. Determine whether the vectors are linearly independent or are linearly dependent in R3. V1 = (-1,2, 1), v2 = (0,3,-2), V3 = (1,4,-1) Solution:
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...