Unknown operator that performs action on a matrix

[81THE1]

Homework Statement

write the matrices M which, when acting on A, divides the second row by a factor a, while leaving the other rows unchanged

Homework Equations

I solved a question on the Gauss-Jordan inversion which showed converting the matrix to the identity would also turn the identity into the inverse; I was thinking for this problem I would take the inversion of A and multiply it by my desired vector to give my answer? Is there a simpler way to do this? assuming my way is correct...

The Attempt at a Solution

Thanks

 

[Dick]

If by 'acting on' you mean the product M*A, then it's a lot easier than you think. The identity matrix doesn't change A at all. Change one entry in the identity matrix so it does what you want.

 

[81THE1]

This is where I am struggling...

I can not seem to find the term to change, and rather than guessing at a solution I want to be able to solve the problem as there is a part b also that will require the same methodology.

A|x> = <alpha| ... If i were to multiply both sides by the inverse of A, it would appear that |x> would be left and that would be my answer, is this correct? If so, it seems like solving the inverse of A would be painfully long. Do you agree, or can i simply just take its transpose?

 

[81THE1]

I see my problem now I think...I was going A * M, not M * A...

If I want to change the second row, now all I have to do is manipulate the second term of the identity matrix to be 1/alpha.

When I reversed them, switching the second one was manipulating the columns...not the rows.

Thanks for your response!