is the rank rank of a 4 x 5 matrix whose null space is three

is the rank rank of a 4 x 5 matrix whose null space is three 5 dimensional?

Solution

According to Rank Nullity Theorem,

The Rank Nullity theorem is defined as the number of columns(A) is equal to rank and null space

Number of Columns(Matrix) = Rankof(4X5 matrix) + Null Space

Since it is a 4X5 matrix, hence number of columns is 5 =>

5 = Rankof(4X5 matrix) + 3

Rankof(4X5 matrix) = 2

Hence rank of matrix is equal to 2