Problem 9, the answer is not G i) only Let v_1 = (-1, -1, 1) and v_2 = (1, 2, 0)

Question

Problem 9, the answer is not G i) only

Let v_1 = (-1, -1, 1) and v_2 = (1, 2, 0). Which of the following vectors are in span {v_1, v_2}? (i) (0, 1, 1) (ii) (1, 3, 2) (iii) (1, 4, 2) (ii) only (i) and (iii) only (iii) only all of them none of them (i) and (ii) only (i) only (ii) and (iii) only Which of the following sets of vectors are independent? (i) (-1, -1, 1), (1, 2, 0), (0, 1, 1) (ii) (-1, -1, 1), (1, 2, 0), (1, 3, 2) (iii) (-1, -1, 1), (1, 2, 0), (1, 4, 2) none of them (i) and (ii) only (iii) only (ii) only (ii) and (iii) only (i) all of them (i) only

Explanation / Answer

9. Let A =

-1

1

0

1

1

-1

2

1

3

4

1

0

1

2

2

The RREF of A is

1

0

1

0

2

0

1

1

0

3

0

0

0

1

0

Apparently, the vector ( 1,3,2) is not in span{v1,v2}. The other 2 vectors are in span{v1,v2}. Option B is the correct answer.

10. (i) It is apprent from the problem 9 above that (0,1,1) = (-1,-1,1)+ (1,2,0). Hence the set is linearly dependent.

      (ii) It is apprent from the problem 9 above that the vector (1,3,2) cannot be expressed as a linear combination of (-1,-1,1)+ (1,2,0) and that the given set is linearly independent.

     (iii) It is apprent from the problem 9 above that (1,4,2) = 2(-1,-1,1)+ 3(1,2,0). Hence the set is linearly dependent.

Option D is the correct answer.

-1

1

0

1

1

-1

2

1

3

4

1

0

1

2

2

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