5. Consider, data involving the variable $x_{ij}$, where $i$ is the subscript denoting the row position and $j$ is the subscript denoting the column position: ($n$: row; $m$ columns). (6 points).
$\sum_{i=1}^{n} \sum_{j=1}^{m} x_{ij} = (x_{11} + x_{12} + ... + ... + x_{1m}) + (x_{21} + x_{22} + ... + x_{2m}) + (x_{31} + x_{32} + ... + x_{3m}) + ... + (x_{n1} + x_{n2} + ... + x_{nm})$
With the following values of $x_{ij}$:
Column ($j$)
($x_{ij}$)
1 2 3
1 10 12 9
Row ($i$)
2 4 34 13
3 5 16 28
4 35 2 42
5 4 27 8
Calculate and \"translate\" (i.e.: write it out in words):
a. $\sum_{i=1}^{n} \sum_{j=1}^{m} x_{ij}$
b. $(x_{43})^2$
c. $\sum_{i=1}^{3} x_{i1}$
d. $\sum_{j=1}^{3} x_{2j}$
e. $(x_{22})^2 + (x_{32})^2$
f. $(x_{22} + x_{32})^2$
