@Kitonum 

Dear;

I think the correct code should be:

P:=<seq(`<|>`(Matrix(M) $ N-1-k,E,H $ k),k=N-1..0,-1)>;

@Kitonum 

Hi Dear

The result is incorrect:
M:=3:  N:=2:
>
> H:=1/N*Matrix(M,{seq((i,1)=t[f]^i/i, i=1..M)});
>
> E:=1/N*Matrix(M, {seq((i,i+1)=1/i, i=1..M-1)});
>
> P:=<seq(`<|>`(Matrix(M) $ N-1-k,E,H $ k),k=M-1..0,-1)>;
                           [1/2 t[f]     0    0]
                           [                   ]
                           [        2          ]
                      H := [1/4 t[f]     0    0]
                           [                   ]
                           [        3          ]
                           [1/6 t[f]     0    0]


                             [0    1/2     0 ]
                             [               ]
                        E := [0     0     1/4]
                             [               ]
                             [0     0      0 ]

Error, (in Matrix) this entry is too wide or too narrow: Matrix(3, 6, [[...],[...],[...]], datatype = anything)

@Carl Love 

Ok...thanks.. I have forgoten it..

@Kitonum 

Dear;

It seems that this code is incorrect..be cause for N=2 and M=3 it produces wrong matrix...

@Kitonum 
thanks a lot...this is what i want..

@Kitonum 

Thanks a lot...

@Mac Dude 

Thanks...that is what I want.....I am grateful of all

@Kitonum 

Thanks dear

but this only gives:

RTABLE(256942340,MATRIX([[Int(1/9*t,t = 0 .. 1)], [Int(-5/9*t,t = 0 .. 1)], [Int(7/9*t,t = 0 .. 1)], [Int(1/9*t,t = 0 .. 1)], [Int(-5/9*t,t = 0 .. 1)], [Int(7/9*t,t = 0 .. 1)], [Int(1/9*t,t = 0 .. 1)], [Int(-5/9*t,t = 0 .. 1)], [Int(7/9*t,t = 0 .. 1)]]),Vector[column]);

and the value of integral is not considered. however I need the numerical value of integral too.

Morever I want to have the result of integral as another vector with same dimension as V1 or V2.

thanks again

best wishes

Mahmood

@Preben Alsholm 

Dear;

please view following attached codes:

p1.mws
p2.mws

in p1 program we have approximate sin(t) while N=3 suninterval and in p2 we do this for 1(as a constant function) but in p1 the result is:

namely the right 3 subinterval but in p2 we have:

where we don't have sunintervals as [0,0.33333] , [0.33333,0.6666667] , [0.6666667,1].

so what is the problem???

@Preben Alsholm 

but i want following form
[1, PIECEWISE([0, t < 0],[c[1,0]+2*c[1,1]*t+4*c[1,2]*t^2, t < 1/2],[c[2,0]+2*c[2,1]*t-c[2,1]+4*c[2,2]*t^2-4*c[2,2]*t+c[2,2], t < 1],[0, 1 <= t])];

or
[1, PIECEWISE([0, t < 0],[c[1,0]+4*c[1,1]*t, t < 1/4],[c[2,0]+4*c[2,1]*t-c[2,1], t < 1/2],[c[3,0]+4*c[3,1]*t-2*c[3,1], t < 3/4],[c[4,0]+4*c[4,1]*t-3*c[4,1], t < 1],[0, 1 <= t])];
and this appears with sqrt(int((g2(t)-g1(t))^2, t=0..1)):
now i an mixed up....

please help me

@Kitonum 

Hi dears
Thank you very much. you have written the answer of question correct and accurately. Good luck and be full of happiness

@acer 

Hi. thanks alot....

that is completely true...

@Kitonum 

so thanks.....great answer and simple one

Hi all.

thanks alot for your nice and so helpful comments.

i want to have another matrix from above matrix as follow

where we have

and

how can i do it?

again i am grateful of all.

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

@Thomas Richard 

hi. thanks. it was helpful