As usual, you will need to submit two files: a MATLAB M-file (with a .m extension) for thefirst 2 questions and a Word or PDF file for question 3. Put your answers to questions 1 and 2as comments in the M-file (following a % sign). Make sure your answers to 3 are appropriatelyformatted. We start with some useful MATLAB commands. Part 1: MatLab Required
1. Solve the following system using the method of matrix inversion: 5.21 + 2.62 - 4.14 + 15 = 6 3.11 + 12 - 2.23 – 4.15 = 3 -21 +3.213 + 14 +5.25 = 2.11 + 3.12 + 13 + 4.14 - Iz = 0 12+ 13 – 214 +3.25 = 1
2. Use the lu command in MatLab to find the LU factorization for the coefficient matrix in question 1. Use this LU factorization to to solve the system in question 1. Is the solution you obtained using the LU factorization the same as the one you obtained using a matrix inverse?
3(a). Determine whether w is in the column space of A, the null space of A, both, or neither, [ -8 5 -2 0 -5 2 1 -2 where w= and A=1 | 10 -8 6 -3 13 -2 0
(b). Use the rank command in MatLab to find the rank of A. Then find the dimension of the null space of A without finding the null space directly.