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Hello

I need some help solving the next question:

u,v,w are linearly independent vectors in a vector space V.

the vectors:

2u+4v+aw

u+2v

2u+bv

are linearly independent when:

1. a is not 0

2. b is not 4

3. a is not 0 OR b is not 4

4. a is not 0, and every value of b

5. a is not 0 AND b is not 4

first of all I noticed that answers 1 and 4 are the same.

I also know that x*v+y*u+z*w=0 implies x=y=z=0

but what next ?

I need some help solving the next question:

u,v,w are linearly independent vectors in a vector space V.

the vectors:

2u+4v+aw

u+2v

2u+bv

are linearly independent when:

1. a is not 0

2. b is not 4

3. a is not 0 OR b is not 4

4. a is not 0, and every value of b

5. a is not 0 AND b is not 4

first of all I noticed that answers 1 and 4 are the same.

I also know that x*v+y*u+z*w=0 implies x=y=z=0

but what next ?

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