Question

Let \[ S=\{(2,5),\ (3,7),\ (4,-9),\ (-8,3)\}. \] Then:

• A. \(S\) is linearly independent
• B. \(S\) is linearly dependent
• C. \(S - \{(4, -9)\}\) is linearly independent
• D. \(S - \{(-8, 3)\}\) is linearly independent

Hint:

To solve vector dependency questions quickly, count the number of vectors and compare it to their dimension.
If there are more vectors than dimensions, the set is always linearly dependent.

Answer 1

The Correct Option is B