Develop your own M-file to determine the Cholesky factorization of a symmetric matrix without pivoting. That is, develop a function that is passed the symmetric matrix and returns the matrix [U]. Test your function by using it to solve the system in Prob. 10.8 and use the built-in function chol to confirm that your function is working properly.

Data From Problem 10.8

(a) Perform a Cholesky factorization of the following symmetric system by hand:

(b) Verify your hand calculation with the built-in chol function. 

(c) Employ the results of the factorization [U] to determine the solution for the right-hand-side vector.

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