Lec 9 - Echelon
January 23, 2012
- All rows that
have at least non-zero entry are above rows with only zeros.
- The leftmost
non-zero entry in a row is a 1, called a leading one.
- The leading one
in a row is to the right of the leading one in any row above it.
- Any column
containing a leading one has it as its only non-zero entry.
(Note: Every Matrix
has a UNIQUE RREF)
Since there is no
choice of variables, this system is inconsistent.
The solution set of
the system is
The solution set is
We must solve the
A system of linear
equations is homogeneous if the
RHS contains only zeros.
ERPs on a homogeneous system will not change the RHS. We just perform EROs on
the coefficient matrix.
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