Determine if Linearly Dependent B={[[-10,2],[5,-2.5]]}

Problem

B={[−10,2],[5,−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 set containing a single vector. A set {V} is linearly dependent if and only if V is the zero vector.

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

V=[[−10,2],[5,−2.5]]

4. Observe that V≠[[0,0],[0,0]] because at least one entry (in fact, all entries) is non-zero.

5. Conclude that since the single vector in the set is not the zero vector, the set is linearly independent, not linearly dependent.

Final Answer

Linearly Dependent=False

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