Thread: Nullspace

Ax=b
a) calculate the nullspace Null(A) and
b) give the general solution of the system Ax=b or state that the system inconsistent.
For b) write in the form x= p+y where p is a particular solution and y ranges across Null (A)

A=1 1 0 2
2 1 1 -2
2 2 2 1

b= 12
0
14

Originally Posted by Rui

Ax=b
a) calculate the nullspace Null(A) and
b) give the general solution of the system Ax=b or state that the system inconsistent.
For b) write in the form x= p+y where p is a particular solution and y ranges across Null (A)

A=1 1 0 2
2 1 1 -2
2 2 2 1

b= 12
0
14

To find the Null space solve the matrix equation Ax=0



now is then


so the vector that spans the Null Space is



solving the system Ax=b



A particualr solution is


so finally we get all solutions are of the form