Hey there! I have a question regarding a Worked Example b.(d), Chapter 4.1 in Strang's LA book. It is not clear to me why the nullspace bases and rowspace basis are taken as (1,1,-1). Why do we take -1 of a rowspace basis? I know it adds up just fine, just the geometry of it is not clear

Question

Hey there!  I have a question regarding a Worked Example b.(d), Chapter 4.1 in Strang's LA book.  It is not clear to me why the nullspace bases and rowspace basis are taken as (1,1,-1).  Why do we take -1 of a rowspace basis?  I know it adds up just fine, just the geometry of it is not clear

anonymous · Answer

Ok sorry its trivial, just taking the sum of the nullspace bases with coefficient 1 and  solving for the coefficient of a row space basis gives -1.  Clear.