Help with least squares

Question

Find the least squares solution of the system AX=B. 

 

Where A = a 4X3 matrix {[1 -1 1] [1 1 1] [0 1 1] [1 0 1] } and b = a 4X1 matrix {[2 1 0 2]}.

 

I have calculated A^⊥A which ={[3 0 3] [0 3 1] [3 1 4]} (a 3 by 3 matrix). and calculated A^⊥b  which = [5 -1 5] (a 3X1 matrix).

 

I am not sure what do do after calculating both of these?

Answer 1

If A, X & B are matrices, A being (n by n), X & B being (n b y 1), then X = A^-1B.

 

So let's say you find A inverse, either on a calculator or by hand.  Then multiply to solve for X.

 

If you meant A^-1B when you typed A⊥b then you have found X = (x, y, z) = (5, -1, 5)