Q34. - Algebra 2

Question

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

 

34. Write a matrix that represents how many more people died as a result of lightning than hurricanes for each year.

Step-by-Step Solution

Answer

The matrix that represents how many more people died as a result of lightning than hurricanes for each year is $\left[\begin{array}{c}15\\ 41\\ 35\\ 27\\ 51\end{array}\right]$. 

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 death due to hurricanes and lightning

Represent the data for deaths due to hurricanes and lightning for each year 1996 to 2000.

$\begin{array}{l}\text{ Lightning}\\ X=\begin{array}{c}1996\\ 1997\\ 1998\\ 1999\\ 2000\end{array}\left[\begin{array}{c}52\\ 42\\ 44\\ 46\\ 51\end{array}\right]\end{array}$  and,

$\begin{array}{l}\text{ Hurricanes}\\ Y=\begin{array}{c}1996\\ 1997\\ 1998\\ 1999\\ 2000\end{array}\left[\begin{array}{c}37\\ 1\\ 9\\ 19\\ 0\end{array}\right]\end{array}$

Step 3 - Write the difference of X and Y matrices

In order to find how many more people died as a result of lightning than hurricanes for each year subtract matrix Y from matrix X and simplify.

$\begin{array}{c}\text{ Lightning Hurricanes}\\ X-Y=\begin{array}{c}1996\\ 1997\\ 1998\\ 1999\\ 2000\end{array}\left[\begin{array}{c}52\\ 42\\ 44\\ 46\\ 51\end{array}\right]-\left[\begin{array}{c}37\\ 1\\ 9\\ 19\\ 0\end{array}\right]\\ =\left[\begin{array}{c}52-37\\ 42-1\\ 44-9\\ 46-19\\ 51-0\end{array}\right]\\ =\left[\begin{array}{c}15\\ 41\\ 35\\ 27\\ 51\end{array}\right]\end{array}$

Therefore, the obtained column matrix represents the difference in the deaths due to lightning and hurricanes.