how to determine if its linearly independent? can anyone explain it? thanks! Sup

Question

how to determine if its linearly independent? can anyone explain it? thanks!

Suppose that vectors v1, v2, v3 are such that -8v1 + 8v2 +8v3 = 0. Are the three vectors linearly independent? Suppose that vectors v1, v2, v3 are such that -8v1 + 8v2 +8v3 = 0. Are the three vectors linearly independent? Suppose that vectors v1, v2, v3, v4 are such that -8v1 + 8v2 = 8v3 - 4v4. Are the four vectors linearly independent? Suppose that vectors v1, v2, v3, v4 are such that -8v1 = 8v3 - 4v4. Are the four vectors linearly independent? Suppose that vectors v1, v2, v3, v4 are such that -8v1 = 8v4. Are the four vectors linearly independent? Suppose that vectors v1, v2, v3, v4 are such that -8v1 + 8v2 + 8v3 = 8v2 + 8v3 - 4v4. Are the four vectors linearly independent?

Explanation / Answer

No. No. Yes. Yes. Yes. Yes. If they are linearly dependent then v1,v2,v3....vn are proportional to some constant K.

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