Least Square Solution(zeros in one row)

[rey242]

Homework Statement

Give a least squares solution to Ax=C and give the residual error

A=
-1, 1, 2;
1, -1, 0;
1, -1, 2;

C=
-1;
-1;
2;

Homework Equations

Residual Error= |Ax-C|

The Attempt at a Solution

I have done an RREF on the Transpose of A times A augmented with the Transpose of A time C and got this:
1, -1, 0, 2/3;
0, 0, 1, 1/4;
0, 0, 0, 0;

I'm not sure what I should do about the bottom row... I know that SHOULD be always an LSQ but it doesn't seem to come out. I know that bottom row indicates an infinite amount of solutions but not sure how to proceed next. Please help

 

[rey242]

Does anyone have any clue?

If it helps, I tried to set the third variable as a number and first and second as equations in terms of each other (i.e 1st in terms of 2nd).

 

[hotvette]

I presume this is a linear algebra class and you've learned about rank and rank deficiency. Is A full rank?

 

[rey242]

not in precise terms...I know the columm space of A is 3x2. I looked up rank in wikipedia...

 

[hotvette]

I suggest you look at the 2nd equation. What does that tell you? Then, look at the 1st equation. It may help to write them out.