week 3 problem 1 to 8

Write a function called odd_index that takes a matrix, M, as input argument and returns a matrix that contains only those elements of M that are in odd rows and columns. In other words, it would return the elements of M at indices (1,1), (1,3), (1,5), …, (3,1), (3,3), (3,5), …, etc. Note that both the row and the column of an element must be odd to be included in the output. The following would not be returned: (1,2), (2,1), (2,2) because either the row or the column or both are even. As an example, if M were a 5-by-8 matrix, then the output must be 3-by-4 because the function omits rows 2 and 4 of M and it also omits columns 2, 4, 6, and 8 of M.
Write a function called int_col that has one input argument, a positive integer n that is greater than 1, and one output argument v that is a column vector of length n containing all the positive integers smaller than or equal to n, arranged in such a way that no element of the vector equals its own index. In other words, v(k) is not equal to k for any valid index k.
Suppose we have a pile of coins. Write a function called rich that computes how much money we have. It takes one input argument that is a row vector whose 4 elements specify the number of pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) that we have (in the order listed here). The output of the function is the value of the total in dollars (not cents). For example, if we had five coins, four quarters and a penny, the answer would be 1.01
Write a function called light_time that takes as input a row vector of distances in miles and returns two row vectors of the same length. Each element of the first output argument is the time in minutes that light would take to travel the distance specified by the corresponding element of the input vector. To check your math, it takes a little more than 8 minutes for sunlight to reach Earth which is 92.9 million miles away. The second output contains the input distances converted to kilometers. Assume that the speed of light is 300,000 km/s and that one mile equals 1.609 km. Write a function called pitty that takes a matrix called ab as an input argument. The matrix ab has exactly two columns. The function should return a column vector c that contains positive values each of which satisfies the Pythagorean Theorem, a2 + b2 = c2, for the corresponding row of ab assuming that the two elements on each row of ab correspond to one pair, a and b, respectively, in the theorem. Note that the built-in MATLAB function sqrt computes the square root and you are allowed to use it.
Write a function called bottom_left that takes two inputs: a matrix N and a scalar n, in that order, where each dimension of N is greater than or equal to n. The function returns the n-by-n square array at the bottom left corner of N.
Write a function called mean_squares that returns mm, which is the mean of the squares of the first nn positive integers, where nn is a positive integer and is the only input argument. For example, if nn is 5, your function needs to compute the average of the numbers 1, 4, 9, 16, and 25. You may use any built-in functions including, for example, sum.
Write a function called hulk that takes a row vector v as an input and returns a matrix H whose first column consist of the elements of v, whose second column consists of the squares of the elements of v, and whose third column consists of the cubes of the elements v. For example, if you call the function likes this, A = hulk(1:3) , then A will be [ 1 1 1; 2 4 8; 3 9 27 ] .