MATRIX DEFINITIONS, REVIEWED  

1. Write the $2 × 2$ and $4 × 4$ identity matrices.

   Hint (a):

   Recall that an identity matrix has $1$s on the diagonal from upper left to lower right and $0$s elsewhere.

2. State the dimensions of each of the following matrices:

   1. $\left[ \begin{array} { l l } { 1 } & { 3 } \\ { 4 } & { 7 } \\ { 2 } & { 6 } \end{array} \right]$ 

   2. $\left[ \begin{array} { c c c c } { 1 } & { - 1 } & { 2 } & { - 2 } \\ { 4 } & { x } & { y } & { 7 } \\ { - 9 } & { 5 } & { \pi } & { 2 } \end{array} \right]$ 

   3. $\left[ \begin{array} { l l } { 2 } & { 3 } \end{array} \right]$ 

   
   

   Hint (b):

   $\text{dimensions: rows} ⨯ \text{columns}$

3. In part (i) above, identify $m_{1,1}, m_{2,1},$ and $m_{1,2}$.

   Hint (c):

   $m_{2,1}$ means the entry in the second row, first column.