Let A be a 6 times 4 matrix with linearly independent column

Let A be a 6 times 4 matrix with linearly independent columns. What can we say about Null A?

Solution

A has 6 x4 matrix with linearly independent columns

So, if 4 columns are independent i.e has pivots

Then Null(A) = 6 -4 = 2    --- ( maximum)

If min. A has 2 independent columns ie.e 2 pivots

Then Null(A) = 6- 2 = 4