Linear independence is a core linear algebra concept used to tell whether a set of vectors contains any redundancy. In this task, you’ll implement a simple checker that decides if a list of vectors is linearly independent. Formally, a set of vectors $\{\mathbf{v}_1, \dots, \mathbf{v}_k\}$ is linearly independent if the equation:

has only the trivial solution $c_1 = \dots = c_k = 0$.

Requirements

Implement the function

Rules:

• Use the definition: vectors are linearly independent iff the only solution to (A\mathbf{c}=\mathbf{0}) is (\mathbf{c}=\mathbf{0}), where (A) has the vectors as columns.
• Build matrix (A) from the input list and determine independence via rank: independent iff (\text{rank}(A)=k).
• Return a single boolean (True/False).
• Do not use symbolic math libraries or prebuilt “independence” helpers; rely on NumPy linear algebra (e.g., np.linalg.matrix_rank).

Example

Output: