Row Space and Column Space

Row Space and Column Space

Example

Row Space

[1 1 1]

[2 1 3]

Row Space

[1 1 1]

[2 1 3]

Column Space

Column Space

[1 1]T

[3 1]T

[2 1]T

Null Space

Example

Row Space

[-2 1 1]T

[2 1 3]

Row Space

[-2 1 1]T

[2 1 3]

Effects of Row Operations

Theorem

Theorem

Example

Theorem

Rank

Nullity

The Rank-Nullity Theorem

The Consistency Theorem

Theorem

Solution Set

x0

v1

v2

Theorem