Matrix Properties / Features

Fun Class Activity:

1. Consider the matrix: 16.
   $M = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ j & k & l \end{bmatrix}.$
   1. What is the size of $M$?
   2. What is $m_{2,3}$ equal to?
   3. List the elements of $\text{diag}(M)$.
2. On slide 8, we introduced multiple notations for a matrix element, but said that we will use only $a_{i,j}$.
   1. Explain one problem that one of the other notations, $a_{ij}$, might impose. [Hint: On what row and column is the element $a_{132}$ located?]
   2. Provide one easy solution to this problem (other than using the $a_{i,j}$ notation.)