To transform a matrix to the identity, , you multiply it by the inverse .
So the question is really, "Find the inverse of L and of U."
I am new at matrices and algebra. Kindly help me out to solve the problem from the first chapter of my textbook.
For a lower triangular matrix L and an upper triangular matrix U of order three with unit diagonal elements determine P such that
(a) LP = PL = I
(b) UP = PU = I
Are you given specific matrices L and U? This seems a very general problem which is going to have a very complicated solution if the off diagonal elements of L and U are "generic". Further, as Fernando Revilla says, you are really asked for a matrix that is the inverse of both L and U. For general L and U, that will not exist.
Actually, this problem is *not* that hard, provided it is two separate problems. The second one, for example, is to find U^{-1}, where:
.
you should know (hopefully) that the product of two upper-triangular matrices with diagonal entries of 1, is another such matrix. since I (the identity matrix) is also upper triangular, with diagonal entries all 1, it seems reasonable to conjecture that U^{-1} is also upper-triangular with 1's on the diagonal. so we want to solve THIS equation:
for x,y and z, in terms of a,b and c. you can do this.