Echelon (rung of a ladder in French, meaning steps, rank.
The echelon method is one by which the matrix is reduced to the upper triangular form, resembling steps. The backward pass will enable all unknowns to be evaluated, if the system is soluble.
The row echelon form is the result of the reduction such that the leading element (the first non-zero element from the left) of each row is reduced to 1.0, and that the leading element is to the right of that of the preceding rows.
As an example:
x+y=3 ....(1)
3x-y=1 ....(2)
x+y = 3 ....(1)A
0x-4y = -8 (1)B (2)-3(1)
x+y = 3 ....(1)C
0x+y = 2 ...(2)C
Equations (1)C and (2)C are now in row-echelon form.
from which we can do the backward substitution to get
y=2,
x=1.
From (3)
y=767/5/76
Use the echelon method to solve the following system.
x/5+3y =31
2x-y/5=8
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