Math-305, Numerical Methods & Matrices
Section 2.3(b):   More on Determinants and Singular Matrices

Dr. K. G. TeBeest
You should have already worked this example of how to use Maple to factor matrix A into LU form.
(Use Maple's LUdecomp command to check your work when appropriate.)

  1. Factor the given matrix A into LU form:

    3 –5 7 4
    –9 16 –16 –3
    27 –39 93 98
    6 –5 39 115

    Then use L and U to solve the system:

    3 –5 7 4
    –9 16 –16 –3
    27 –39 93 98
    6 –5 39 115
    x1
    x2
    x3
    x4
    		  =  
    –14
    87
    160
    321
    1. What happened?
    2. What is det(A)?
    3. Is A singular or nonsingular?
    4. Show that the set    x1 = –5,   x2 = 7,   x3 = 4,   x4 = 2    is a solution of the system.
    5. Show that the set    x1 = 27,   x2 = 22,   x3 = 1,   x4 = 2    is a solution of the system.
    6. Show that the set    x1 = –37,   x2 = –8,   x3 = 7,   x4 = 2    is a solution of the system.
    7. How many solutions must the system therefore have?

  2. Try to solve the same system by Gauss elimination.
    What happened?

  3. Use Maple's inverse command to attempt to invert matrix A.
    What is the result?

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