# Why this equation can't solve

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?

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

x=(aT*a)-1*B

Homework Helper
Okay, for which item are you trying to solve.

$$x = a - 1b$$

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

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

Mark44
Mentor
Okay, for which item are you trying to solve.

$$x = a - 1b$$

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 = (ATA)-1b.

Homework Helper
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 = (ATA)-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
Homework Helper
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). ATA is a 20 x 20 matrix and so is (ATA)-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 = (ATA)-1 ATb.

HallsofIvy