Thread: Matrix Proof

I need to prove that these determinants are equals.
Note: these are determinants, not matrices, I just don't know how to set them up as determinants using the math code...

= (1- )

This tells me that I need to somehow get (1- ) multiplied into the determinant. I know that to get that out, one would have to multiply a row by (1- ), or possibly (1-t) on two different rows... Am I thinking it the right direction?

Originally Posted by Hellreaver

I need to prove that these determinants are equals.
Note: these are determinants, not matrices, I just don't know how to set them up as determinants using the math code...

= (1- )

This tells me that I need to somehow get (1- ) multiplied into the determinant. I know that to get that out, one would have to multiply a row by (1- ), or possibly (1-t) on two different rows... Am I thinking it the right direction?

Consider the matrix .

Apply the row operation R1 --> R1 + t R2 on matrix A to get matrix B: det(B) = det(A).

Apply the row operation (1 - t^2) R2 + R1 --> R2 on matrix B to get matrix C: det(C) = (1 - t^2) det(B) ......

Originally Posted by mr fantastic

Consider the matrix .

Apply the row operation R1 --> R1 + t R2 on matrix A to get matrix B: det(B) = det(A).

Apply the row operation (1 - t^2) R2 + R1 --> R2 on matrix B to get matrix C: det(C) = (1 - t^2) det(B) ......

Ok, that's tricky. Thank you so much!