Ref Lecture Notes p.35-3
Evaluate the remaining coefficient of Matrix by using degrees of Freedom
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
Ref Lecture Notes p.35-4
Find the inverse of given Matrix
A =
1 0 0 0
0 1 0 0
1 1 1 1
0 1 2 3
%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
Ref Lecture Notes p.35-4
Identify the basis functions
where
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
Ref Lecture Notes p.36-1
We have to show that s is the function of t (s = s(t) )
We have (from p.35-1 eq (1))
so
Hence Proved