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====== Math 445 Lab #2 ======

**Instructions:** Use the ''diary'' feature to create a diary file to record your Matlab session. Run ''format compact'' to save electrons and ultimately trees. Solve the problem set, then turn the diary off. Edit the diary with a text editor to remove mistakes, then print out the diary, write the names of your work group members on it, and turn it in. 

//Please distribute the work among the group members, and make sure that everyone understand everything!//

**Problem 1:** In Matlab, create a 2 x 2 matrix 
<latex>
A = \left[
\begin{array}{cc}
5 & 2 \\
-1 & 3 
\end{array}
\right]
</latex>
and a 2-d vector
<latex>
b = \left[
\begin{array}{cc}
1 \\
2
\end{array}
\right]
</latex>.
What vector $x$ satisfies $Ax=b$?

**Problem 2:** Save your $A$ and $x$ to disk (hard drive) and run //clear all// to clear all the variables from Matlab. Then load
$A$ and $x$ from disk and compute the product $Ax$ to verify that $Ax=b$. 

**Problem 3:** Use Matlab to solve the problem. Nilanjana has 50 coins worth $9.10. They're all quarters and nickels. How many nickels and how many quarters does she have? Verify that your answer solves the problem. 

**Problem 4:** Use Matlab to solve the problem. Flying against the wind, a plane travels 2880 miles in 4.5 hours. Flying with the wind, it travels the same distance in 4 hours. How fast is the wind? How fast is the plane on a windless day?

**Problem 5:** From //Numerical Computing with Matlab// by Clive Moler.

{{:gibson:teaching:fall-2012:math445:truss2.png?direct&600}}

{{:gibson:teaching:fall-2012:math445:truss3.png?direct&600}}

{{:gibson:teaching:fall-2012:math445:truss4.png?direct&600}}


**Problem 6:** (bonus) Use Matlab to solve the problem. A man is three times as old as his son was at the time when the father was twice as old as his son will be two years from now. Find the present age of each if their ages now sum to 55.
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