prove or make an example:
Assume we convert a square matrix A to an upper triangular matrix U by using multiplication method, i.e. EA = U, where E is the elimination matrix. Show that E-l is a lower triangular matrix. Therefore we can decompose A to a lower and upper triangular matrix, .A = LU. (Hint: you can show this by using the example that I solved in lecture 2. There, I explained how you can compute the inverse of the elimination matrix quickly.)
Show transcribed image text Assume we convert a square matrix A to an upper triangular matrix U by using multiplication method, i.e. EA = U, where E is the elimination matrix. Show that E-l is a lower triangular matrix. Therefore we can decompose A to a lower and upper triangular matrix, .A = LU. (Hint: you can show this by using the example that I solved in lecture 2. There, I explained how you can compute the inverse of the elimination matrix quickly.)