matrix algerba questions

Matrices, though they may appear weird objects at first, are a very important tool in expressing and discussing problems which arise from real life cases.

Our first example deals with economics. Indeed, consider two families A and B (though we may easily take more than two). Every month, the two families have expenses such as: utilities, health, entertainment, food, etc… Let us restrict ourselves to: food, utilities, and health. How would one represent the data collected? Many ways are available but one of them has an advantage of combining the data so that it is easy to manipulate them. Indeed, we will write the data as follows:

<img src=”http://www.sosmath.com/matrix/matrix0/img1.gif” alt=”\begin{displaymath}\mbox{Month}=\left(\begin{array}{cccc}
\mbox{Family}&\mbox{Fo…
…ies}&\mbox{Health} \\
A&a&b&c\\
B&d&e&f\\
\end{array}\right)\end{displaymath}”>

If we have no problem confusing the names and what the expenses are, then we may write

<img src=”http://www.sosmath.com/matrix/matrix0/img2.gif” alt=”\begin{displaymath}\mbox{Month}=\left(\begin{array}{cccc}
a&b&c\\
d&e&f\\
\end{array}\right)\end{displaymath}”>

This is what we call aMatrix. The size of the matrix, as a block, is defined by the number ofRowsan