Show that the Doolittle method of LU Decomposition does not work on the matrix
([2,2,1],[1,1,1],[3,2,1]).
Perform a row exchange so that the Doolittle method now works.
Show with an example that a non-invertible 3x3 matrix A whose leading principal minors
of order 1 and 2 are non-zero has a Doolittle factorization.
Perform Cholesky Decomposition on the matrix
([4,6,2],[6,10,3],[2,3,5])
and hence solve the system of equations
4x+6y+2z=4
6x+10y+3z=4
2x+3y+5z=6.
Show that the Doolittle method of LU Decomposition does not work on the matrix
Perform a row exchange so that the Doolittle method now works.
Show with an example that a non-invertible 3x3 matrix A whose leading principal minors
of order 1 and 2 are non-zero has a Doolittle factorization.
Perform Cholesky Decomposition on the matrix
6
2
6
10 3
3
and hence solve the system of equations
4x+6y+2z=4
6x+10y+3z=4
2x+3y+5z=6.