please help me solve this and show each step The statement is either true in all
ID: 3185096 • Letter: P
Question
please help me solve this and show each step
The statement is either true in all cases or false. If false, construct a specific example to show that the statement is not always true. If v4 are in R4 and v3 2v+2, then (v,. V2. V3. V4) is linearly dependent. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. True. Because v -2v1+2. V4 must be the zero vector. Thus, the set of vectors is linearly dependent O B. True. Ifc2c2-1, c3 -1, and c4-0, then c,v1+.4V4. The set of vectors is linearly dependent O C. True. The vector v is a linear combination of v, and vg, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent O D. False. If v1 3and v4 then v3 2V1 + V2 and (v1, V2, V3, V4 is linearly independent.Explanation / Answer
Answer :
True. Since v3 = 2v1 + v2 .
The linear combination is 2v1 + 1.v2 - 1.v3 + 0.v4 = 0
So the set of vectors is linearly dependent
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