Finding Least Square Solutions for Singular Matrices

[Punkyc7]

Find the least square solutions x* of the system Ax=bA=[1 3
2 6]

b=[5
0]A^tAx=A^tbSo I get down to
[5 15 [x1 [5
15 45] x2] = 15]

so i get [1
0]

The book says the solution is
[1-3s
s]

not sure were that came from

 

[lanedance]

can you explain your method?

 

[Punkyc7]

Just plug into the formula the only problem is that the matrix I get by multiplying A transpose A cannot not be inverted

 

[hotvette]

Just plug into the formula the only problem is that the matrix I get by multiplying A transpose A cannot not be inverted

That's because A^TA is singular, which in this case means an infinite number of solutions. If you multiply things out by hand you can get the answer.