Q33. - Algebra 2

Question

For Exercises 33-35, use the table that shows the total number of deaths due to severe weather.

 

Find the total number of deaths due to severe weather for each year expressed as a column matrix.

Step-by-Step Solution

Answer

The column matrices representing the total number due to severe weather for each year are:

$\begin{array}{l}\text{ 1996}\\ A=\begin{array}{c}\text{Lightning}\\ \text{Tornadoes}\\ \text{Floods}\\ \text{Hurricanes}\end{array}\left[\begin{array}{c}52\\ 25\\ 131\\ 37\end{array}\right]\end{array}$     $\begin{array}{l}\text{ 1997}\\ B=\begin{array}{c}\text{Lightning}\\ \text{Tornadoes}\\ \text{Floods}\\ \text{Hurricanes}\end{array}\left[\begin{array}{c}42\\ 67\\ 118\\ 1\end{array}\right]\end{array}$     $\begin{array}{l}\text{ 1998}\\ C=\begin{array}{c}\text{Lightning}\\ \text{Tornadoes}\\ \text{Floods}\\ \text{Hurricanes}\end{array}\left[\begin{array}{c}44\\ 130\\ 136\\ 9\end{array}\right]\end{array}$

$\begin{array}{l}\text{ 1999}\\ D=\begin{array}{c}\text{Lightning}\\ \text{Tornadoes}\\ \text{Floods}\\ \text{Hurricanes}\end{array}\left[\begin{array}{c}46\\ 94\\ 68\\ 19\end{array}\right]\end{array}$  and   $\begin{array}{l}\text{ 2000}\\ E=\begin{array}{c}\text{Lightning}\\ \text{Tornadoes}\\ \text{Floods}\\ \text{Hurricanes}\end{array}\left[\begin{array}{c}51\\ 29\\ 37\\ 0\end{array}\right]\end{array}$

Step 1 - Define the concept of organizing data in matrix

A matrix is a rectangular array of variables or constants in horizontal rows and vertical columns, usually enclosed in brackets. Data is organized in such a way that each position has a purpose. Each value of the matrix is called an element.

Step 2 - Write the matrix depicting data for the years 1996 and 1997

The data in the table can be organized in five column matrices of order $4\times 1$ for years 1996 to 2000. Let the first and second matrix representing the data for the years 1996 and 1997 be A and B. Then, 

$\begin{array}{l}\text{ 1996}\\ A=\begin{array}{c}\text{Lightning}\\ \text{Tornadoes}\\ \text{Floods}\\ \text{Hurricanes}\end{array}\left[\begin{array}{c}52\\ 25\\ 131\\ 37\end{array}\right]\end{array}$and,

$\begin{array}{l}\text{ 1997}\\ B=\begin{array}{c}\text{Lightning}\\ \text{Tornadoes}\\ \text{Floods}\\ \text{Hurricanes}\end{array}\left[\begin{array}{c}42\\ 67\\ 118\\ 1\end{array}\right]\end{array}$

Step 3 - Write the matrix depicting data for the year 1998, 1999 and 2000

Let the first and second matrix representing the data for the years 1998, 1999 and 2000 be C, D and E. Then, 

$\begin{array}{l}\text{ 1998}\\ C=\begin{array}{c}\text{Lightning}\\ \text{Tornadoes}\\ \text{Floods}\\ \text{Hurricanes}\end{array}\left[\begin{array}{c}44\\ 130\\ 136\\ 9\end{array}\right]\end{array}$  $\begin{array}{l}\text{ 1999}\\ D=\begin{array}{c}\text{Lightning}\\ \text{Tornadoes}\\ \text{Floods}\\ \text{Hurricanes}\end{array}\left[\begin{array}{c}46\\ 94\\ 68\\ 19\end{array}\right]\end{array}$ and  $\begin{array}{l}\text{ 2000}\\ E=\begin{array}{c}\text{Lightning}\\ \text{Tornadoes}\\ \text{Floods}\\ \text{Hurricanes}\end{array}\left[\begin{array}{c}51\\ 29\\ 37\\ 0\end{array}\right]\end{array}$