For each of the following, provide an answer in Matlab-digestable syntax

1. Assign the value 0.00014 to the variable //x//, using compact scientific notation.

2. Set the variable //x// to a vector whose components are the even numbers between 14 and 36.

3. Set the variable //x// to 200 evenly spaced points between 0 and 2.

4. Produce a plot of //y = x^2 - 2x + 3// for the //x// of the previous problem. Label the axes.

5. Plot //tan(x)// versus //x// for 200 evenly spaced points between 0 and 1.57 ≈ pi/2, using
a logarithmic scale on the //y// axis. 

6. Plot //sin(x)// and //cos(x)// for 200 evenly spaced points between -π and π, on the same plot,
using red for //sin(x)// and blue for //cos(x)//. Add a legend that indicates which function is which color.

7. Produce a vector whose components are random integers between 0 and 10, inclusive.

8. Produce a vector whose components are random real numbers between 0 and 10, inclusive.

9. Show how you would solve the following system of equations with Matlab

<code>
  x + 2y -  z =   5
 3x +  y + 6z =  37
-3x +  y + 2z = -11
</code>

10. Write a conditional expression that is true if scalar variables //x// and //y// are both nonzero 
and false otherwise.

11. Set variable //A// to a 3 x 5 matrix of zeros.

12. Set variable //A// to a 4 x 7 matrix of random real numbers, using a guassian (normal) distribution.

13. Write a conditional expression that is true if a matrix //A// is square and false otherwise.

14. Write a conditional expression that is true if either //x// or //y// is an integer.



Write a Matlab function that

15. returns 1 (true) if its argument is divisible by 3 and 0 (false) if it's not. 

16. takes a vector //x// as input and returns 1 if the components of //x// are sorted
in ascending order, 0 if not.

17. finds a zero of another function using the bisection search algorithm.

18. computes the product //y = Ax// of an //m x n// matrix //A// and an //n x 1// vector //x//, according the formula
<latex>
y_i = \sum_{j=1}^n A_{ij} x_j
</latex>