Description

Introduction to Programming with MATLAB
Lesson 4
• Unless otherwise indicated, your function should not print anything to the Command Window, but your
function will not be counted incorrect if it does.
• Note that you are not required to use the suggested names of input variables and output variables, but you must use the specified function names.
• Finally, read the instructions on the web page on how to test your functions with the auto-­‐grader program provided, and what to submit to Coursera to get credit.

1. Write a function called quadrants that takes as its input argument a scalar integer named n. The function returns Q, a 2n-­‐by-­‐2n matrix. Q consists of four n-­‐by-­‐n submatrices. The elements of the submatrix in the top left corner are all 1s, the elements of the submatrix at the top right are 2s, the elements in the bottom left are 3s, and the elements in the bottom right are 4s.
2. Write a function called checkerboard that takes as input two positive integer scalars, n and m, in that order. The function must create and return board, which is an n-­‐by-­‐m matrix. Every element of board is either 0 or 1. The first element, board(1,1) is 1. No direct neighbors in the matrix, vertically or horizontally, can be equal. That is, a 1 element cannot have 1 immediately preceding or following it in the same row or column.
3. Write a function called randomness that takes three input arguments: limit, n, and m, in that order. The function returns an n-­‐by-­‐m matrix of uniformly distributed random integers between 1 and limit inclusive. You are not allowed to use randi, but you can use rand. You will also find the built-­‐in function floor useful for obtaining integers. To make sure that your result is indeed uniformly distributed, test the output of the function by using the built-­‐in function hist, which plots a histogram.
4. Write a function called mtable that returns mt an n-­‐by-­‐m matrix corresponding to the multiplication table (n is the first and m is the second input argument). That is, the element of mt at row ii and column jj equals to ii*jj. The function also has a second output, s, a scalar that equals the sum of all the elements of mt.
5. Write a function called identity that creates a square identity matrix, which is a matrix whose elements are 0 except for the elements on the diagonal (from top left to bottom right) which have a value of 1. The diagonal consists of those elements whose row and column indexes are the same: (1,1), (2,2), etc. The function takes one positive integer input argument, which is the size of the matrix, and returns the matrix itself as an output argument. For example, identity(4) must return a 4-­‐by-­‐4 identity matrix. You are not allowed to use the built-­‐in eye or diag functions. (Hint: you can index into a matrix with a single index and MATLAB will handle it as if it was a vector using column-­‐major order.)