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2. Which of the following sets of vectors in R3 are linearly dependent?

2.  Which of the following sets of vectors in R3 are linearly dependent?
a)  (4, -1, 2), (-4, 10, 2)
b)  (-3, 0, 4), (5, -1, 2), (1, 1, 3)
c)  (8, -1, 3), (4, 0, 1)
d)  (-2, 0, 1), (3, 2, 5), (6, -1, 1), (7, 0, -2)
4.  Which of the following sets of vectors in P2 are linearly dependent?
a)  2 - x + 4x2,  3 + 6x + 2x2,  2 + 10x - 4x2
b)  3 + x + x2,  2 - x + 5x2,  4 - 3x2
c)  6 - x2,  1 + x + 4x2
d)  1 + 3x + 3x2,  x + 4x2,  5 + 6x + 3x2,  7 + 2x - x2
12.  Show that if {v1, v2, v3} is linearly dependent set of vectors in a vector space V, and v4 is any vector in V, then {v1, v2, v3, v4} is also linear dependent.

General Vector Spaces – Linear Independence
2. Which of the following sets of vectors in R3 are linearly dependent?
a) (4, -1, 2), (-4, 10, 2)
b) (-3, 0, 4), (5, -1, 2), (1, 1, 3)
c) (8, -1, 3), (4, 0, 1)
d) (-2, 0, 1), (3, 2, 5), (6, -1, 1), (7, 0, -2)
4. Which of the following sets of vectors in P2 are linearly dependent?
a) 2 – x + 4x2, 3 + 6x + 2x2, 2 + 10x – 4x2
b) 3 + x + x2, 2 – x + 5x2, 4 – 3x2
c) 6 – x2, 1 + x + 4x2
d) 1 + 3x + 3x2, x + 4x2, 5 + 6x + 3x2, 7 + 2x – x2
12. Show that if {v1, v2, v3} is linearly dependent set of vectors in a
vector space V, and v4 is any vector in V, then {v1, v2, v3, v4} is also
linear dependent.

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