a = 3;
b = 1.5;
m = 100;
g = 9.8;
door(a,b,m,g)
Case 1: Statically determinate system

A1 =

     1     0     0
     0     1     0
     0     0     1


detA1 =

     1


rankA1 =

     3


condA1 =

     1


rcondA1 =

     1


b1 =

  1.0e+003 *

         0
    0.9800
    1.4700

Solution using backslash operator

x1 =

  1.0e+003 *

         0
    0.9800
    1.4700

Solution using matrix inverse

invA1 =

     1     0     0
     0     1     0
     0     0     1


x1 =

  1.0e+003 *

         0
    0.9800
    1.4700

Case 2: Overdetermined system

A2 =

     1     0     0
     0     1     0
     0     0     1
     1     0     0
     0     1     0
     0     0     1
     1     0     0
     0     1     0
     0     0     1


rankA2 =

     3


condA2 =

     1


b2 =

  1.0e+003 *

         0
    0.9800
    1.4700
    0.0000
    0.9702
    1.4847
   -0.0000
    0.9898
    1.4553

Least-squares solution using backslash operator

x2 =

  1.0e+003 *

         0
    0.9800
    1.4700

??? Undefined function or variable 'x'.

Error in ==> <a href="error:F:\EGM4344\Lecture 17\door.m,67,1">door at 67</a>
errors = A2*x-b2

door(a,b,m,g)
Case 1: Statically determinate system

A1 =

     1     0     0
     0     1     0
     0     0     1


detA1 =

     1


rankA1 =

     3


condA1 =

     1


rcondA1 =

     1


b1 =

  1.0e+003 *

         0
    0.9800
    1.4700

Solution using backslash operator

x1 =

  1.0e+003 *

         0
    0.9800
    1.4700

Solution using matrix inverse

invA1 =

     1     0     0
     0     1     0
     0     0     1


x1 =

  1.0e+003 *

         0
    0.9800
    1.4700

Case 2: Overdetermined system

A2 =

     1     0     0
     0     1     0
     0     0     1
     1     0     0
     0     1     0
     0     0     1
     1     0     0
     0     1     0
     0     0     1


rankA2 =

     3


condA2 =

     1


b2 =

  1.0e+003 *

         0
    0.9800
    1.4700
    0.0000
    0.9702
    1.4847
   -0.0000
    0.9898
    1.4553

Least-squares solution using backslash operator

x2 =

  1.0e+003 *

         0
    0.9800
    1.4700


errors =

         0
    0.0000
         0
   -0.0100
    9.8000
  -14.7000
    0.0100
   -9.8000
   14.7000

Case 3: Underdetermined system

A3 =

    1.0000         0         0    1.0000         0         0
         0    1.0000         0         0    1.0000         0
         0         0    1.0000    1.5000         0    1.0000


rankA3 =

     3


condA3 =

    2.0000


b3 =

  1.0e+003 *

         0
    0.9800
    1.4700

Solution using backslash operator

x3 =

 -980.0000
  980.0000
         0
  980.0000
         0
         0


normx3 =

  1.6974e+003

Solution using matrix pseudo inverse

pinvA3 =

    0.6800         0   -0.2400
         0    0.5000         0
   -0.2400         0    0.3200
    0.3200         0    0.2400
         0    0.5000         0
   -0.2400         0    0.3200


x3 =

 -352.8000
  490.0000
  470.4000
  352.8000
  490.0000
  470.4000


normx3 =

  1.0824e+003

Solution using quadratic programming optimization
Optimization terminated: relative (projected) residual
 of PCG iteration <= OPTIONS.TolPCG.

xqp =

 -352.8000
  490.0000
  470.4000
  352.8000
  490.0000
  470.4000

Asym = [ 1 2 3; 2 5 3; 0 5 1]

Asym =

     1     2     3
     2     5     3
     0     5     1

Asym = [ 1 2 3; 2 5 3; 3 3 1]

Asym =

     1     2     3
     2     5     3
     3     3     1

Adiag = eye(4)

Adiag =

     1     0     0     0
     0     1     0     0
     0     0     1     0
     0     0     0     1

Aupper = [1 0 0; 2 5 0; 3 3 1]

Aupper =

     1     0     0
     2     5     0
     3     3     1

Alower = Aupper

Alower =

     1     0     0
     2     5     0
     3     3     1

Abanded = [1 2 0; 3 5 7; 0 4 1]

Abanded =

     1     2     0
     3     5     7
     0     4     1