@Carl Love really sorry to disturbe you again. Actually I did a little mistake. Order of block matrix should be M1M2×M1M2 which have null and F1 matrices of order M2×M2.

Like M1=2 and M2 = 2

Matrix(2, 2, {(1, 1) = O, (1, 2) = O, (2, 1) = F1[2, 1], (2, 2) = O})

where null and F1 matrices of order 2 by 2

and for M1=2 and M2= 3

Matrix(2, 2, {(1, 1) = O, (1, 2) = O, (2, 1) = F1[2, 1], (2, 2) = O})

where null and F1 matrices of order 3 by 3

for M1=3 and M2=2 then we have block matrix

Matrix(3, 3, {(1, 1) = O, (1, 2) = O, (1, 3) = O, (2, 1) = F1[2, 1], (2, 2) = O, (2, 3) = O, (3, 1) = O, (3, 2) = F1[3, 2], (3, 3) = O})

where null and F1 matrices of order 2 by 2

@Carl Love thanks I got it :)
Now I want to define a block matrix F like

restart; with(LinearAlgebra); with(linalg);

M1 := 3; M2 := 3;

OM2 := Matrix(1 .. M2, 1 .. M2, shape = zero);

IM2 := IdentityMatrix(M2)
nu := 1;

printlevel := 3;

for r1 from 2 while r1 <= M1 do

for s1 while s1 <= r1-1 do

if type(r1+s1, odd) then

F1[r1, s1] := (2*(2*s1-2+2*nu))*IM2

end if

end do end do;

F is M1 by M2 block matrix have entries F1[r1, s1] others entries are null matrix (OM2)

It did it for M1=M2=3 and define F manully like

F := blockmatrix(M1, M2, [OM2, OM2, OM2, F1[2, 1], OM2, OM2, OM2, F1[3, 2], OM2])
But I want to know general way how to define F if M1 and M2 large like 10.

@Carl Love thanks for you kind response. May be meaning is same but I used the block matrix termonology. Anyhow, how to define it for any value of M.

Thanks @Kitonum for your positive and quick response!

@acer @Carl Love @Kitonum @Preben Alsholm

@tomleslie thanks for your kind response!

@Carl Love thanks for your kind response!

@mmcdara 

thank you so much for your help.

@acer @Carl Love @Kitonum

@Kitonum dear I want to compare the coefficient of like powers of exponential function of the following attached file. When I run the program I got the following error

Error, invalid input: coeff received 1, which is not valid for its 2nd argument, x
Help.mw

@acer @Carl Love @Kitonum

@Carl Love @tomleslie thanks for your valuable comments

@vv how we replace exp(eta*k2) with Z^k2?

@vv Thanks your vaulable comments. Now, I want to construct system of equations by comparing the likes powers of x^i*y^j*t^k1*exp(k2*eta) for an expression H1 present in attached file. Please see the fix my problem. I shall be very thankful for your kind help.

Help.mw

@acer @Carl Love @Kitonum @Preben Alsholm