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.