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
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. 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