Thread: trying to figure out how to prove two matrices are equal

Ok, so I am trying to prove that one matrix equals another without finding determinates. The first matrix is
(1, a, bc)
(1, b, ac)
(1, c, ab)

I need to figure out how to make that equal to:
(1, a, a^2)
(1, b, b^2)
(1, c, c^2)

I need to do this using column operations, so far I've tried multiplying the 2nd column by abc and subtracting the 3rd column to get the 3rd column, but I can't figure out how to finish off and get the squared letters by themeselves...

Thanks to anyone who takes time to figure this out, it's a big help

Originally Posted by snoboarder2k6

Ok, so I am trying to prove that one matrix equals another without finding determinates. The first matrix is
(1, a, bc)
(1, b, ac)
(1, c, ab)

I need to figure out how to make that equal to:
(1, a, a^2)
(1, b, b^2)
(1, c, c^2)

I need to do this using column operations, so far I've tried multiplying the 2nd column by abc and subtracting the 3rd column to get the 3rd column, but I can't figure out how to finish off and get the squared letters by themeselves...

Thanks to anyone who takes time to figure this out, it's a big help

two matrices are equal if their corresponding entries are equal

well, yeah, but not knowing the values of a, b, and c, you can't just say bc = a^2 etc.

thanks though

Originally Posted by snoboarder2k6

well, yeah, but not knowing the values of a, b, and c, you can't just say bc = a^2 etc.

thanks though

well, a = b = c works...

can you not state that as a solution?

true, but the object of the problem is to prove that the first matrix equals the second matrix generally, not just by stating one particular case.