Problem 3Which of the following sets of vectors are linearindependent?O(A)(1,1,0),(1,0,1),(0,1,1)O(B)(1,1,2,-2),(3,0,3,-4),(-1,2,1,0)O(C)(1,1,2,-2),(2,3,0,-1),(-1,2,1,0)O(D)(2,-2,2), (1,2,-1),(2,-5,4)

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Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 69E: Find a basis for R2 that includes the vector (2,2).

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Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check your work against the answers in the back of the book. Write w=(7,2,4) as a linear combination of the vectors v1, v2 and v3 if possible. v1=(2,1,0), v2=(1,1,0), v3=(0,0,6)
Find a basis for R2 that includes the vector (2,2).
Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)
2. If , and the vector is drawn with its tail at the point, find the coordinates of the point at the head of .
Determine whether each vector is a scalar multiple of z=(3,2,5). a v=(92,3,152) b w=(9,6,15)
skip the first 3 thank you
For what value(s) of a are the following vectors linearly independent: (1,5,-2), (0,6,a) and (3,13,-3)?
Oo Ob OF 1. Which of the following is a set of linearly independent vectors? a. (1,2,1),(1,2,2), (2,4,2) b. (1,2,2),(1,1,1) c. (1,1,1),(2,2,2)
(i) Prove that (1, 2, 1) , (2, 1, 5) , (1, –4,7) is linear dependent subset of R³. (ii) Determine whether the vector (1,6, 2) is a linear combination of the vectors (1,2, –1), (3, 1, 1), and (-4,0, 6). (Include all the steps in your reasoning.).
Please include all steps and details
(a) Determine whether W= (0, 5, 4) can be expressed as a linear combination of the vectors v1 = (-2,9,1) v3= (-3, 2, 1) and v3= (1, 7, 5) or not.
1. Write the vector H- 16 as a linear combination of the vectors and D

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Problem 3 Which of the following sets of vectors are linear independent? O(A)(1,1,0),(1,0,1),(0,1,1) O(B)(1,1,2,-2),(3,0,3,-4),(-1,2,1,0) O(C)(1,1,2,-2),(2,3,0,-1),(-1,2,1,0) O(D)(2,-2,2),(1,2,-1),(2,-5,4)