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Section 6 Wrap Up Questions

  1. Give an example of three different \(2\times 2\) matrices that have determinant \(0\text{.}\)
  2. Give an example of three different matrices that have determinant \(1\text{.}\)
  3. We have defined \(n\times n\) matrices as linear transformations from \({\mathbb R}^n\) to \({\mathbb R}^n\text{,}\) but the definition naturally generalizes to other matrices. When generalizing this definition, from what dimension space does an \(m\times n\) matrix define a linear transformation, and what is the dimension it maps to?
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