Untitled

We revisit the previous example using algebra to express the row operations on

A = [2 0 4 3 ; -4 5 -7 -10 ; 1 15 2 -4.5 ; -2 0 2 -13];

We use the identity and its columns heavily.

I = eye(4);

The first step is to put a zero in the (2,1) location using a multiple of row 1:

mult21 = A(2,1)/A(1,1);
L21 = I - mult21*I(:,2)*I(:,1)';
A = L21*A
A = 
   2.0000e+00            0   4.0000e+00   3.0000e+00
            0   5.0000e+00   1.0000e+00  -4.0000e+00
   1.0000e+00   1.5000e+01   2.0000e+00  -4.5000e+00
  -2.0000e+00            0   2.0000e+00  -1.3000e+01

We repeat the process for the (3,1) and (4,1) entries.

mult31 = A(3,1)/A(1,1);
L31 = I - mult31*I(:,3)*I(:,1)';
A = L31*A;
mult41 = A(4,1)/A(1,1);
L41 = I - mult41*I(:,4)*I(:,1)';
A = L41*A
A = 
     2     0     4     3
     0     5     1    -4
     0    15     0    -6
     0     0     6   -10

And so on, following the pattern as before.