Question

Find the basis for the row space, columnspace, and nullspace for the following matrix.

Row 1 {3,4,0,7}

Row 2 {1,-5,2,-2}

Row 3 {-1,4,0,3}

Row 4 {1,-1,2,2}

Answer 1

Solution:

The null space is the set of solution to

By   

By

By

By

The basis for Null space is

In the row reduced form of   the first , second and third column form the pivot columns.

    the first , second and third column of the original matrix form the basis for the cokumn space of

Basis for

  

  The basis for Row space of     is