Matrix Rank 2

1
Matrix Rank

• Rank Definition
• Rank Computation
• Rank Properties
• Rank and Linear System AXB

2
Rank Definition

• Column Rank
• is the maximum number of linearly independent
  column vectors in A
• Row Rank
• is the maximum number of linearly independent row
  vectors in A
• Theorem Column Rank Row Rank

3
Rank Computation

• Ex. Find Rank(A) where
• By applying Gauss-Elimination
• Rank(A)2 (number of non-zero rows after
  Gauss-Elimination)