According to the Rank-Nullity Theorem, if a matrix has 7 columns and a rank of 3, what is its nullity?
Show answer
4
The Rank-Nullity Theorem states that for an m x n matrix, rank(A) + nullity(A) = n. Here, 3 + 4 = 7, where 7 is the number of columns (the dimension of the domain).
Also asked as:
- Using the Rank-Nullity Theorem, what is the nullity of a matrix with 7 columns and a rank of 3?