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
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.