1. Write a Python code to: 1. a. Find the inverse of the following matrix. Show that the matrix you found satisfies the definition of a multiplicative inverse.
(AA' = A'A= 1) A [i 4 3 21 1 7 4 5 =I 72 5 3 1 (1 3 29 [4 3 2] 3 -1 2 61
b. Find a 3 x 4 matrix X such that 5 6 3 X = 7 4 1 5 . 3 5 2 5 2 4 1
Show that the matrix X satisfies the above equation.
2. Following the instructions given in the text, section 3.4.4, use Python to solve problems 3.4.9 and 3.4.10, i. e., enter the Python commands to determine the eigenvalues, eigenvectors and characteristic polynomial for the 3 x 3 matrices given in these problems. From these results, write the general solutions in vector form. (Note that Python is not used in writing the general solutions; just apply the ideas discussed in class and write (by hand) the general solutions.)