Multiplying and finding inverse of a matrix.

I = [9; -3; 10; -10]

G = [0.3 0 -0.2 0; 0 0.25 -0.25 0; -0.2 -0.25 0.95 0; 0 0 0 0.05]

Invs(G)*I

Answer 1

[madhan ravi]

It’s inv() not invs()

Answer 2

[Sam Chak]

Hi @Omar

Just wanted to share the three methods I sometimes use to compute the matrix inverse.

G  = [0.3  0    -0.2  0; 
      0    0.25 -0.25 0; 
     -0.2 -0.25  0.95 0; 
      0    0     0    0.05]

G = 4×4

0.3000 0 -0.2000 0 0 0.2500 -0.2500 0 -0.2000 -0.2500 0.9500 0 0 0 0 0.0500

%% Method 1: direct inverse function
inv(G)

ans = 4×4

4.1176 1.1765 1.1765 0 1.1765 5.7647 1.7647 0 1.1765 1.7647 1.7647 0 0 0 0 20.0000

%% Method 2: Matrix left division
G\eye(length(G))

ans = 4×4

4.1176 1.1765 1.1765 0 1.1765 5.7647 1.7647 0 1.1765 1.7647 1.7647 0 0 0 0 20.0000

%% Method 3: Reduced row echelon form 
A  = [G eye(length(G))];
R  = rref(A)

R = 4×8

1.0000 0 0 0 4.1176 1.1765 1.1765 0 0 1.0000 0 0 1.1765 5.7647 1.7647 0 0 0 1.0000 0 1.1765 1.7647 1.7647 0 0 0 0 1.0000 0 0 0 20.0000

iG = R(:,5:end)

iG = 4×4

4.1176 1.1765 1.1765 0 1.1765 5.7647 1.7647 0 1.1765 1.7647 1.7647 0 0 0 0 20.0000