70.3k views
4 votes
Show that these vectors are linearly dependent and find a non-trivial linear combination of them that results in the zero vector.

User Zsmaster
by
8.4k points

1 Answer

1 vote

Final answer:

To show that vectors are linearly dependent, we need to find a non-trivial linear combination that results in the zero vector.

Step-by-step explanation:

To show that vectors are linearly dependent, we need to find a non-trivial linear combination that results in the zero vector. Let's say we have three vectors: v1, v2, and v3. If there exist scalars a, b, and c (not all zero) such that av1 + bv2 + cv3 = 0, then the vectors are linearly dependent. To find a non-trivial linear combination, we can set a = 1, b = 1, and c = -1. This gives v1 + v2 - v3 = 0, which is a non-trivial linear combination that results in the zero vector.

User Yan Zhu
by
7.3k points