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gibson:teaching:fall-2013:math445:hw3

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 of length 13 whose components are random integers between 0 and 10, inclusive.

8. Produce a vector of length 13 whose components are random real numbers between 0 and 10, inclusive.

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

  x + 2y -  z =   5
3x +  y + 6z =  37
-3x +  y + 2z = -11

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. computes the product y = Ax of an m x n matrix A and an n x 1 vector x, according the formula

A few more problems, added 1/14/2013

18. Set vector v to the 3rd column of matrix A.

19. Set vector v to the 4th row of matrix A.

20. Set vector v to the first 3 entries in the 7th row of A.

21. Set the 4th row of the 8 x 5 matrix A to (1, 2, 9, 5, 0).

22. Set the 2nd column of the 4 x 3 matrix A to a column vector with entries (3, 0, -1, 5).

23. Zero all the entries in the last column of a matrix A.

24. Produce a contour plot of where x and y range from -10 to 10. Label the axes.

A few more problems, added late 10/14/2013. You don't have to turn these in, but they are fair game for the exam. I will add more example problems over the next few days.

25. Write an expression that returns the positive elements of a vector v.

26. Write an expression that returns the sum of the positive elements of a vector v.

27. Write an expression that returns the number of positive elements in a vector v.

Even more practice problems! Hooray! added 10/22/3013

28. Write a function that computes the factorial of an integer n using a while loop.

29. Write an isPrime(n) function that returns 1 (true) is n is prime and 0 (false) if n is not prime. Don't worry about making the test efficient or doing it with integer arithmetic.

30. Write a function that returns a vector of all the integer divisors of an integer n. Again, don't worry about efficiency or integer arithmetic.