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A Matrix Method to Solve a System of
n
Linear
Equations in
n
unknowns:
1.
Write the augmented matrix that represents the
system.
2.
Perform row operations to simplify the augmented
matrix to one having
zeros below the
diagonal
of
the coefficient portion of the matrix.
(An entry is on the diagonal of the coefficient
portion of the matrix if it is located in row i and
column i
for some positive integer
i
≤
n.)
If the augmented matrix is equivalent to a matrix
with
zeros below the diagonal
and all
nonzero
entries on the diagonal
, then the corresponding
system has a
unique solution
.
If the aumented matrix is equivalent to a matrix
with
zeros below the diagonal
and
at least one
zero on
the diagonal
, then the corresponding
system
does not have a unique solution
In this case, examination of the rows which contain
a zero on the diagonal entry will determine
whether the corresponding system has no solution
or an infinite number of solutions.
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The system of equations represented by the following
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 Fall '11
 Kutter
 Algebra, Equations

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