Selected problems from Attaway 3rd edition, chapters 1 and 2.

**Problem 1:** Create the following vectors twice, once using **linspace** and once using the colon operator.

  1 2 3 4 5 6 7 8 9 10
  
  2 7 12
  
**Problem 2:** Use the colon and transpose operators to create a column vector that has values -1 to 1 in steps of 0.2.

**Problem 3:** Given a vector //v// of arbitrary length, write an expression that evaluates to the odd-numbered elements of //v//. Test your expression on vectors //v// of both even and odd length.

**Problem 4:** Given a vector //v// of arbitrary length, write assignment statements that store the first half of //v// in a vector //v1// and the second half in a vector //v2//. Make sure your assignment statements work for //v// of both even and odd length. 

**Problem 5:** Create a 4 x 2 matrix of all zeros and store it in a variable. Then replace the second row of the matrix with a 3 and a 6. 

**Problem 6:**  Create a 3 x 5 matrix of random real numbers, and then delete the third row. 

**Problem 7:** What are the values of the following expressions? Explain why.

  'c' == 'd' - 1 && 2 < 4
  'c' == 'd' - 1 || 2 < 4
  xor('c' == 'd' - 1, 2 < 4)
  10 > 5 > 2
  
**Problem 8:** The value of $\pi^2/6$ can be approximated by the sum of the series

<latex>
1 + 1/2^2 + 1/3^2 + 1/4^2 + \ldots
</latex>

Write a one-line Matlab expression that evaluates the sum for the first $n$ terms. Test it for a few values of $n$ and compare to $\pi^2/6$.

**Problem 9:** A vector //v// stores hours worked and hourly wages sequentially for a number of employees. For example

<code>
  v = [33 10.5 40 18 20 7.5]
</code>

would specify three employees, the first working for 33 hours at %%$10.50/hr%%, the second 40 hours at %%$18/hr%%, etc. For an arbitrarily long //v//, write code that would separate //v// into an //h// vector of hours worked and a //r// vector of hourly wage rates, and then compute a //w// vector of wages owed to each employee. Do this as compactly as possible. 


**Problem 10:** Evaluations at a university are scored 1-5, bad to good. However the evaluation forms mistakenly say that 1-5 is good to bad. So the computer program written to analyze evaluations must "reverse" all the evaluation scores. That is,

  evals = [5 3 2 5 5 4 1 2]
  
should really be

  evals = [1 3 4 1 1 2 5 4]
  
Write Matlab code that will reverse an arbitrary //eval// vector to the correct 1-5 scale.