Determine if Linearly Dependent A={[[1,2],[3,4]]}

Problem

A={[1,2],[3,4]}

Solution

1. Identify the set of vectors. The set A contains a single non-zero matrix M=[[1,2],[3,4]]

2. Apply the definition of linear independence for a single vector. A set containing a single vector {v} is linearly dependent if and only if v=0

3. Check if the matrix is the zero matrix. Since at least one entry in M is non-zero (e.g., 1≠0, the matrix is not the zero matrix.

4. Conclude the dependency status. Because M≠0 the set A is linearly independent.

Final Answer

A={[1,2],[3,4]}* is linearly independent

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