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

Dr. Kevin G. TeBeest
  1. Use Gauss elimination 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. You should have already worked this example of how to use Maple to factor matrix A into LU form.

    Use it to factor A into LU form.

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