Question: Algorithm 6.7.1 of the class notes is as follows: 1. We consider the matrix 4 2 -6 4 2 2 -3 1 6 -3 13

Algorithm 6.7.1 of the class notes is as follows: 1. We

Algorithm 6.7.1 of the class notes is as follows:

consider the matrix 4 2 -6 4 2 2 -3 1 6

-3 13 0 4 1 0 30 E R4x4 (a) Calculate the

1. We consider the matrix 4 2 -6 4 2 2 -3 1 6 -3 13 0 4 1 0 30 E R4x4 (a) Calculate the matrix factor R of the Cholesky decomposition A RTR by using Algorithm 6.7.1 of the class notes. (b) Solve for y the lower triangular linear system Ry b where -25' 68 Then solve for x the upper triangular linear system Rz = y and check that x satisfies Ax b. (c) Using the matrix factor R of the Cholesky decomposition of A give the exact value of the determinant det(A) 1. We consider the matrix 4 2 -6 4 2 2 -3 1 6 -3 13 0 4 1 0 30 E R4x4 (a) Calculate the matrix factor R of the Cholesky decomposition A RTR by using Algorithm 6.7.1 of the class notes. (b) Solve for y the lower triangular linear system Ry b where -25' 68 Then solve for x the upper triangular linear system Rz = y and check that x satisfies Ax b. (c) Using the matrix factor R of the Cholesky decomposition of A give the exact value of the determinant det(A)

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