I am having trouble computing this problem in matlab. How do I compute AA^-1 and print out the product where A is the 9x9 matrix?

A=[ai,j] , ai,j=1/i+j-1. So far I have i=4 and j=5

[John D'Errico]

Please don't add answers, when all you want to do is make a comment. In my comment, I even said that was what you are asked to compute. Thus, it seems clear that the homework problem you have been assigned was to...

Compute the 9x9 hilbert matrix, thus the square matrix A(i,j), such that

A(i,j) = 1/(i+j-1)

Then compute the inverse of that matrix and multiply the two. Is the product an identity matrix, as theory suggests it should be? If not, then you might be asked to conjecture as to why it is not so. This might be the subject of further class discussions and/or homework assignments.

Answer 1

[Image Analyst]

Uh,

i=4
j=5

will not do

A=[ai,j]
ai,j=1/i+j-1

I don't know exactly what operation you were hoping for, but that code won't do it. Why don't you try in a for loop over j. Then you'll need to define what ai is. the second line of code only defines j to be (1/i) + j + 1, it does NOT define ai at all, and hence when you try to use it as a row vector in [ai,j] it will fail because ai was never defined.

Also, what exactly is "AA^-1" - can you describe in words what operation(s) this is?

[John D'Errico]

I have a funny feeling you know this, but ... It looks like the goal is to generate a 9x9 Hilbert matrix, then compute the inverse, and multiply the two, seeing if the product is really an identity matrix. The result won't be too close to an identity.

Of course I might guess that hilb(9) is not an acceptable solution to part of the question.

[Image Analyst]

Not sure why this was accepted.

[John D'Errico]

I was surprised too. Surely a reflection of the pure quality of your answers, even when you were totally confused yourself.