6. Are vectors ū= (1,-1,2 %; v = (-1,-1,-1) and W = (-1,-5,1 ) linearly dependent?...
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=...
(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.
Only one option is correct. Being u,v and w linearly dependent vectors of a linear space E. Then : a) u and v are linearly independent . b) u and v are linearly dependent . c) u, u + v and u + w are linearly independent . d) u, u + v and u + w are linearly dependent .
please anyone answer all the questions as soon please 2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
It is given that the vectors ū = [11,0, 6] and ✓ = (-2,0,–27) lie in a linear subspace W of R'. It follows that, also ū = 29, 0, -36) lies in W. This can be seen by writing was a linear combination of ū and V. Determine the numbers x and y so û = x ·ū+y. V. Give your answer in the form x = a 1y=b for two numbers a and b.
(1 point) Let c=1 ). 6 = [-), = [E]. * = [1] Is ū a linear combination of the vectors ū1, ū2 and ū3 ? choose If possible, write ū as a linear combination of the vectors ū1, 72 and 73. For example, the answer ū = 4ū1 + 5ū2 + 6Ū3 would be entered 4v1 + 5v2 + 6v3. If ū cannot be written as a linear combination of the vectors ū1, 72 and 73, enter DNE. ū...
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...
6. Displacement vectors 7 , ū, V, and ū are given below. In the appropriate diagram, draw (a) the projection of 7 onto ū (b) the projection of ū onto ū (c) the projection of ū onto ū. ū ū ū 2 f V w
6 and 7!!! 6. Given the points A - (0,0), B = (5,1),C - (2,6) on the plane. Use a determinant to find the area of the triangle ABC. 7. Let T:V - W be a linear transformation, and let 01,03,...,U, be vectors in V. Suppose that T(u), 7(v2),...,T(v.) are linearly independent. Show that 01,03,.., are linearly independent
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