Find an elementary matrix E such that EAC where A 1 3 0 2 1

Find an elementary matrix E such that EA-C where A = [1 3 0 2 1 5 0 4 -2] and C = [1 2 0 2 13 -1 0 4 -2]

Solution

EA = C

A = 1       3        0

       2       1        5

       0       4       -2

C = 1          3           0

        2         13         -1

        0          4          -2

we have EA = C

we multiply both sides by A^-1

E*A*A^-1 = C*A^-1

E = C*A^-1                 //    A*A^-1 = I

now we calculate A^-1

A^-1 = 11/5        -3/5          -3/2

         -2/5          1/5            1/2

          -4/5          2/5            1/2

now E = C*A^-1

E = 1      0         0

       0      1        3

       0       0       1