Matrix Rank & Nullity

Rank, nullity, and reduced row echelon form

Matrix A

rank(A) + nullity(A) = columns (n)
Rank
2
Nullity
1
Rank–nullity theorem
2 + 1 = 3
Rank-deficientSingular (not invertible)
Reduced row echelon form
1
0
-1
0
1
2
0
0
0
Dimensions
3 × 3
Pivot columns
1, 2
Matrix Rank & NullityBar splitting the 3 columns into a rank part of 2 and a nullity part of 1, shown above the reduced row echelon form with pivot cells highlighted.Rank–nullity theoremRank 2Nullity 110-1012000