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1.
Interchange two rows
2.
Multiply a row by a nonzero real number
3.
Replace a row by its sum with a multiple of another row
Overdetermined System
:
More equations than unknowns. In R
2
each equation represents a line, usually
inconsistent.
Underdetermined System:
A system with fewer equations than unknowns.
Usually consistent with
infinitely many solutions.
Inconsistent System:
A system with no solutions.
Consistent System:
A system with one or infinitely many solutions.
Reduced Row Echelon Form:
1.
If the first nonzero entry in each nonzero row is 1.
2.
If row k does not consists entirely of zeros, the number of leading zero entries in row k+1
is greater than the number of leading zero entries in row k.
3.
If there are rows whose entries are all zero, they are below the rows having nonzero
entries.
Matrixvector multiplication
: If A is an mxn matrix and x is a vector in R
n
then
Ax = x
1
a
1
+ x
2
a
2
+ … + x
n
a
n
Consistency Theorem:
A linear system Ax=b is consistent if and only if b can be written as a linear
combination of the column vectors of A.
MatrixMatrix Multiplication:
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 Spring '08
 RINGHOFER
 Linear Algebra, Algebra, Equations

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