11.22

Write the following set of equations in matrix form:

50 = 5x_3 -7x_2
4x_2 + 7x_3 + 30 = 0
x_1 - 7x_3 = 40 - 3x_2 +5x_1

 Use excel, MATLAB, or Mathcad to solve for the unkowns. In addition,
 compute the transpose and the inverse of the coefficient matrix.

50 = 5x_3 -7x_2 + 0x_1
30 = - 7x_3 - 4x_2 + 0x_1
-40 =  7x_3 - 3x_2 +4x_1




Matlab Code:

A = [5 -7 0; -7 -4 0; 7 -3 4];

B = [50; 30; -40];

X = A\B;

%transpose

TransposeA = A.';

%inverse

inverseA = inv(A);

display(A)

display(B)

display(X)

display(TransposeA)

display(inverseA)

Results

A =

     5    -7     0

    -7    -4     0

     7    -3     4

B =

    50

    30

   -40

X =     

   -0.1449

   -7.2464

  -15.1812

TransposeA =

     5    -7     7

    -7    -4    -3

     0     0     4

inverseA =

    0.0580   -0.1014         0

   -0.1014   -0.0725         0

   -0.1775    0.1232    0.2500

X_1 = -0.1449

X_2 = -7.2464

X_3 = -15.1812