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 â 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 â x + 4x2, 3 + 6x + 2x2, 2 + 10x â 4x2

b) 3 + x + x2, 2 â x + 5x2, 4 â 3x2

c) 6 â x2, 1 + x + 4x2

d) 1 + 3x + 3x2, x + 4x2, 5 + 6x + 3x2, 7 + 2x â 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.

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 â 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 â x + 4x2, 3 + 6x + 2x2, 2 + 10x â 4x2

b) 3 + x + x2, 2 â x + 5x2, 4 â 3x2

c) 6 â x2, 1 + x + 4x2

d) 1 + 3x + 3x2, x + 4x2, 5 + 6x + 3x2, 7 + 2x â 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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