Question: Crouts method factorizes where L is lower triangular and U is upper triangular with diagonal entries (a) Formulas. Obtain formulas for Crouts method similar to

Crout€™s method factorizes where L is lower triangular and U is upper triangular with diagonal entries

(a) Formulas. Obtain formulas for Crout€™s method similar to (4).

(b) Examples. Solve Prob. 5 by Crout€™s method.

(c) Factor the following matrix by the Doolittle, Crout, and Cholesky methods. 

-4 -4 25 4 4 24 2.

(d) Give the formulas for factoring a tridiagonal matrix by Crout€™s method.

(e) When can you obtain Crout€™s factorization from Doolittle€™s by transposition?
Data from Prob. 5

Show the factorization and solve by Doolittle€™s method.

   3x1 +   9x2 +   6x3 =   4.6
18x1 + 48x2 + 39x3 = 27.2
  9x1 - 27x2 + 42x3  =    9.0

-4 -4 25 4 4 24 2.

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