Question

Should be an easy one in MATLAB with a simple proof for part (a). Thanks for the help in checking my answers:

(Pencil-and-paper and MATLAB) L A be a non-singular n x n matrix. Then it has an inverse (a) Let the vectors ui, i 1,2,... n, be the columns of of A-1. Show that the wi satisfy the linear systems Au where v is a vector whose sole nonzero entry is 1 in the ith position. (b) se the above equation to compute A-1. Take A to be a 5 x 5 random matrix, which can be constructed by using the MATLAB command A rand (5). You may use the backslash or lu commands of MATLAB to solve the linear systems for the vi. (c) Check that the product A A recovers the identity matrix I Write a MATLAB script that carries out all the tasks listed above, and prints the results in a properly labelled form. The results should display the matrices A and A 1 and their product

Answer 1

Sample Run:

Raw Paste Code of (b) & (c)

A=rand(5)

%initialize vis
v1=[1; 0; 0; 0; 0];
v2=[0;1; 0; 0; 0];
v3=[0; 0; 1; 0; 0];
v4=[0; 0; 0; 1; 0];
v5=[0; 0; 0; 0; 1];

%use backslash to find ui
u1=A\v1
u2=A\v2
u3=A\v3
u4=A\v4
u5=A\v5

%combine ui to produce A^-1

Ain=[u1 u2 u3 u4 u5]

%to check the value A*Ain=I
I=A*Ain