LEC15

Outline

• Underdetermined systems:
  • A system of $m$ equations in $n$ variables is underdetermined if $n>m$.
  • Since there are more columns than rows, some column will end up without a pivot ⇒ existence of free parameters.
  • When we have free params, we have infinite solutions.
• Overdetermined systems:
  • A system of $m$ equations in $n$ variables is underdetermined if $n<m$.
  • Since there are more rows than columns, some columns will end up with more than one pivot.
  • Most overdetermined systems are inconsistent.
• Homogeneous Systems of Linear Equations.