Pronunciation: /bæk ˈsʌb stɪˌtut ʃən/ ?
Back substitution is an
for solving a
that has been reduced to row-eschelon form, which is an upper triangular matrix:
Since the rows in a matrix represent
equations, and the columns represent variables in those equations, the matrix
can be expressed as the linear system
The value of z
is know, so 3 can be substituted into the equation
just above it:
Now that the values of y
are known, these two
values can be substituted into the first equation:
So the solution to the linear system is:
Cite this article as:
Back Substitution. 2008-11-20. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/b/backsubstitution.html.
2008-11-20: Initial version (McAdams, David.