An Introduction to Matrices

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?