If the nullity of a space of a 7 times 6 matrix A is 5 what

If the nullity of a space of a 7 times 6 matrix A is 5 what is the dimension of Col(A)?

Solution

Let Col(A) = rank (A) = x

Usning rank-nullity theorem,

rank + nullity = Number of columns of matrix (It is given nullity =5 and number of columns =6)

x + 5 = 6

Subtracting 5 from both sides ,

x = 1

So, col(A) = 1