Question & Answer: Write a function m-file to reduce a matrix to a row-echelon form with pivoting. Use this function m-file to reduce the matrices B and C fro…..

(a) R = rref(A) produces the reduced row echelon form of A using Gauss Jordan elimination with partial pivoting.

Say a matris is defied as

a = [1 2 3; 4 5 6; 7 8 10]

Output ,

a =

    1    2    3
    4    5    6
    7    8   10

NOw run the command

R = rref(a)

it will give the ouput like

R =

   1   0   0
   0   1   0
   0   0   1

With partial pivoting

(b) Simmilarly for

B = [2 6 10 -10; 5 15 26 11; -6 19 35 -47]

R = rref(B)

Output ::::

R =

    1.00000    0.00000    0.00000   10.97297
    0.00000    1.00000    0.00000  -65.32432
    0.00000    0.00000    1.00000   36.00000

and

C = [2 6 10 -12; 4 12 20 24; -2 9 33 -7]

R = rref(C)

OUTPUT ::::

R =

   1.00000   0.00000  -3.60000   0.00000
   0.00000   1.00000   2.86667   0.00000
   0.00000   0.00000   0.00000   1.00000