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
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.