Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3...

Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3 = (1, 1, 3) linearly independent or dependent? Since v2 is a scalar multiple of v1, both v1 and v2 are linearly dependent, but what does that say about the linear dependence of the three vectors as a whole?

Expert Solution

Concept : If one vector can be expressed a linear combination of another vectors , then those vectors can be said as Linearly dependent.

If v2 can be expressed as linear combination of v1 and v3 such that,

v2 = a1V1 + a2V2 where at least one of the scalar a1, a2 is non zero

Here,

v2 = 2v1 + 0v3 . Thus , all three vectors are Linearly dependent.

Method 2 :

Colby Messinger answered 2 years ago

if {v1,v2,v3} is a linearly independent set of vectors, then {v1,v2,v3,v4} is too.

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v1=[0,1,4] v2=[-4,-5,7] v3=[14,10,8] b=[16,18,19]. Let v1,v2, and v3 be three nonzero vectors in R3. Suppose v2 is not a scalar multiple of either v1 or v3 and v3 is not a scalar multiple of either v1 or v2. Does it follow that every vector in R3 is in span{v1,v2,v3}?

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Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3...

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