Determine if Linearly Dependent B={[[-1,2],[0,-2.5]]}

Problem

B={[−1,2],[0,−2.5]}

Solution

1. Identify the number of vectors in the set B The set contains exactly one matrix, which we can call V

2. Recall the definition of linear dependence for a single vector. A set containing a single vector is linearly dependent if and only if that vector is the zero vector.

3. Check if the matrix V is the zero matrix.

V=[[−1,2],[0,−2.5]]

4. Observe that V≠[[0,0],[0,0]] because at least one entry is non-zero.

5. Conclude that since the set contains only one non-zero vector, it must be linearly independent.

Final Answer

The set *B* is linearly independent.

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