MATLAB PROJECT 1
The goals of this project are: (1) to be able to input by hand and use MATLAB functions to generate vectors and matrices in MATLAB; (2) to use MATLAB to generate a reduced echelon form for a matrix; (3) to solve a system using the reduced echelon form of its augmented matrix; (4) to investigate the linear dependence of a set of vectors.
PROBLEM 1: Generate a 4x4 matrix based on the birth dates of four people you know and call it A. (Input this by hand; for example, if Time Traveleling Terp was planning to use the birthdate of Gabriel Cramer of Cramer’s rule fame, 31 July 1704, it will have a row or column containing the numbers 31, 07 ,17, 04. Using MATLAB functions, generate B, a 4x4 matrix of ones, a 4x4 matrix of zeroes and I, the 4x4 identity matrix.
Hint: To generate B, O, and I, search for help on the functions zeroes, ones, eye.
PROBLEM 2: Based on the matrices in problem 1, compute the following elements and then explain what they are in the corresponding matrix:
(a) a=A(2,4) ; (i.e. this is the ____ element/row/column of the matrix A)
(b) ac= A(:,4);
(c) ar= A(2,:).
Is it true or false that (d) a*B=B*a and (e) ac*I=I*ac?
Explain your results for Problem 2 points (d) and (e ).
PROBLEM 3: (a) Generate a random 3x5 matrix A with entry integers uniformly between -12 and 12. (b) Put it in reduced echelon form using the command rref. (c) Are the columns of A linearly independent? Why or why not? (d) What is the span of the columns of A?
Base your answer on your result at points 3b and your general knowledge of what the Span of 1, 2, 3 linearly independent vectors should be. Hint: Search for help on the functions rand and randi.
PROBLEM 4: Solve problem 34 section 1.2 pp 23 (same in fourth and fifth edition of Lay’s textbook).
PROBLEM 5: Using MATLAB, solve problem 4 section 1.10 (same in fourth and fifth edition of Lay’s textbook).
