University of Florida/Egm6341/s10.team3.aks/HW6

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(3) Evaluate the rest of the coefficient of matrix[edit]

Ref Lecture Notes p.35-3

Problem Statement[edit]

Evaluate the remaining coefficient of Matrix by using degrees of Freedom


Solution[edit]

We have

such that

where

such that

We know the coefficient of matrix for first two rows from lecture notes p.35-3

Using the equations above we have

Putting the results in matrix form we obtain


(4) Verify the inverse of matrix using Matlab[edit]

Ref Lecture Notes p.35-4

Problem Statement[edit]

Find the inverse of given Matrix

A =

    1     0     0     0
    0     1     0     0
    1     1     1     1
    0     1     2     3

Solution[edit]

 

%Defining Matrix in Matlab%

>> A = [1 0 0 0 ; 0 1 0 0 ; 1 1 1 1 ; 0 1 2 3]

A =

     1     0     0     0
     0     1     0     0
     1     1     1     1
     0     1     2     3

%Taking Inverse of matrix%
>> B = inv (A)

B =

     1     0     0     0
     0     1     0     0
    -3    -2     3    -1
     2     1    -2     1

which is same as the one given on p.35-4

Hence Verified

(5) Identify basis functions and plot them[edit]

Ref Lecture Notes p.35-4

Problem Statement[edit]

Identify the basis functions

where

Solution[edit]

We have

Expanding above we obtain

Inserting above values in first eq we obtain

Comparing both LHS and RHS we obtain

Solving above we obtain basis functions

Below is the plot of above basis functions

Basis function plot.jpg

(6) Show that [edit]

Ref Lecture Notes p.36-1

Problem Statement[edit]

We have to show that s is the function of t (s = s(t) )

Solution[edit]

We have (from p.35-1 eq (1))

so

Hence Proved