Why Does Inverting Matrix A Fail to Solve the Equation?

[jacky_pcs]

I would like to solve equation with x=a-1*b but when I inverse matrix A . It is bad solution to solve (I use mathematica to solve it)(Attach matrix A in excel file).
I want to know why matrix A is bad solution when I inverse??
If I want to solve this equation. How i can do?

 

[statdad]

Is your matrix a square? If not - no inverse. (Although being square is not itself sufficient for an inverse to exist.)

 

[jacky_pcs]

-I use Pseudo method but answer is bad solution
x=(aT*a)-1*B

 

[statdad]

Okay, for which item are you trying to solve.

your equation was
$$x = a - 1b$$

That has nothing to do at all with your "solution" - your result doesn't follow from the equation.

 

[hunt_mat]

Roger Penrose worked on the inverses on non-square matries before relativity.

 

[Mark44]

Okay, for which item are you trying to solve.

your equation was
$$x = a - 1b$$

That has nothing to do at all with your "solution" - your result doesn't follow from the equation.

I believe the OP meant x = A^-1b.

Then he/she revised the above to this: x=(aT*a)-1*B,
which I believe means this: x = (A^TA)^-1b.

 

[statdad]

I believe the OP meant x = A^-1b.

Then he/she revised the above to this: x=(aT*a)-1*B,
which I believe means this: x = (A^TA)^-1b.

Aha - good catch. Of course, this means that the original equation is nowhere to be seen, so it remains impossible to see why this approach fails.

 

[hotvette]

Need to pay attention to dimension. The matrix A has 35 rows and 20 columns (i.e. 35 x 20) and B has 35 rows (i.e. 35 x 1). A^TA is a 20 x 20 matrix and so is (A^TA)^-1. Multiplying a 35 x 1 matrix by a 20 x 20 matrix isn't valid.

This smells like a least squares problem, which means the solution would be x = (A^TA)^-1 A^Tb.

 

[HallsofIvy]

Roger Penrose worked on the inverses on non-square matries before relativity.

What in the world do you mean by this? Roger Penrose wasn't born until 26 years after relativity was developed! Do you mean he worked on them before they were used in relativity?

 

[willem2]

What in the world do you mean by this? Roger Penrose wasn't born until 26 years after relativity was developed! Do you mean he worked on them before they were used in relativity?

Penrose worked those inverses before he worked on relativity