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Unformatted text preview: Review of Linear Algebra & Linear Systems I Joao P. Hespanha 1 Linear Algebra The material reviewed here can be found in [ 2 , Chapter 1] or [ 1 , Chapter 2.2]. Consider the matrix A 1 2 7 2 1 4 1 2 1 1. What does it mean for a A to be nonsingular? 2. Is A nonsingular? 3. How would you compute the inverse of A ? 4. What is the image, rank of a matrix? 5. What is the kernel, nullity of a matrix? 6. Compute bases for the image and kernel of A . 7. How would you do this in MATLAB? 2 LTI Systems Most of the material reviewed here can be found in [ 3 , Lectures 17] or [ 1 , Chapter 2]. Consider the following system 9 x Ax bu , y cx u , (1) where c 1 1 , A 2 1 , b 1 1 . 1. What is the transfer function of this system? 2. How does the transfer function relate system inputs and outputs? 3. How can one find the solution to the system for nonzero initial conditions x t x ? 4. Compute the state transition matrix for this system. How would you compute it for more complicated systems? 5. What is the definition of e At and how would you compute it in MATLAB?...
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- Fall '09