newbie : trouble with calculating inverse of a matrix and = inf ???

[Andy Davidson]

I am trying to calculate the inverse of a matrix. I get this strange answer. Any idea what my problem is? Is there some sort of reference for these kinds of problems?

octave:15> x = [x0' x1' x2']

x =

   1   1   4

   1   2   5

   1   3   6

octave:16> inv(x' * x) 

warning: inverse: matrix singular to machine precision, rcond = 0

ans =

   Inf   Inf   Inf

   Inf   Inf   Inf

   Inf   Inf   Inf

Here is a complete diary of what I am trying to do

thanks in advance

Andy

#

# Least Sq. Regresion

# calculate the paramters for theta using closed form solution

# theta = inv(x' * x) * x' * y

#

#

# create a simple data set from the equation y = 3 + x1 + 2x2 

# to make sure we understand basic linear algebra in Octave

#

octave:2> x1 = [ 1 2 3]

x1 =

   1   2   3

octave:3> x2 = [ 4 5 6];

octave:4> y = 3 + x1 + 2*x2

y =

   12   15   18

#

# create a row vector theta. We already know the parameters of the eq.

#

octave:6> theta = [3; 1; 2]

theta =

   3

   1

   2

octave:10> x = [1 6 7]; # create a new training example

octave:11> x * theta # the expected answer should be 23

ans =  23

#

# begin closed form solution for theta

#

octave:12> x1

x1 =

   1   2   3

octave:13> x2

x2 =

   4   5   6

octave:14> x0 = [1 1 1]

x0 =

   1   1   1

octave:15> x = [x0' x1' x2']

x =

   1   1   4

   1   2   5

   1   3   6

octave:16> inv(x' * x) 

warning: inverse: matrix singular to machine precision, rcond = 0

ans =

   Inf   Inf   Inf

   Inf   Inf   Inf

   Inf   Inf   Inf

octave:17> diary off