actually it is not important for me to be inversible,i just want K2.Vt gives me original equations,
how about first question? can i collect them as i want it?
i am really thankful for your attention and help.

@Carl Love  i want it to collect the expressions that only has a[3]. not the other ones.

for example i want it give me a[1]*a[2]*a[3]+a[3]^3.

i do not want to use for example this command

select(has,eq1,a[3]). i need to use collect beacuse my main problem is another one.

i have 3 equations.

eq1:=a[1](t)*a[2](t)^2+a[2](t)*a[3](t)*a[1]+a[3](t)^3;
eq2:=a[1](t)^3*a[2](t)^2+a[2](t)*a[3](t)+a[2](t)^3;
eq3:=a[1](t)*a[3](t)^2+a[3](t)^2*a[1](t)^3+a[2](t);

i want to write them like this 

<eq1,eq2eq3>;=[3*3 matrix including coefficients]*<a[1],a[2],a[3]>.

i need coefficients matrix.

last time Preben Alsholm helped me,with using equate command,but when range of equations go higher,multiplying the coefficients matrix in coefficients itself does not give me back the original equations.

http://www.mapleprimes.com/questions/149035-Convert-To-Vector-Mode

i need to use another way to produce this matrix,do anyone has any comment that how can i do that?

in fact in the page that i have reffered to,K1.V does not give the original equations for me,not in this 3*3 matrix,
i face problem in 18*18 or higher order matrix, 
here is the code, and 9 of these equations are not correct.problem_2.mws 

i think u should put your system here so that everybody can evaluate the situation better.

@Markiyan Hirnyk i actully do this after that,it made the problem solved. thnx.

@Markiyan Hirnyk i actully do this after that,it made the problem solved. thnx.

@Markiyan Hirnyk thank u,really.
i have another question, how can i use these values for further equations ?
i mean after solving these equations, when i type a[1](0.0001) it simply returns just itself,not the result that fsolve find,what should i do here? actually i want to assign the values that fsolve has found to the unkowns,what should i do ?

@Markiyan Hirnyk thank u,really.
i have another question, how can i use these values for further equations ?
i mean after solving these equations, when i type a[1](0.0001) it simply returns just itself,not the result that fsolve find,what should i do here? actually i want to assign the values that fsolve has found to the unkowns,what should i do ?

@Mathematix u want the answer to the third question ?! but the problem are not the same.since u have written exp(-3) but it is exp(-3*x) . your answer seems to be somewhat simpler but for more skillful member i think.
but both are doing the same thing.

if you write it in this way,(exp(-3*x)) u can easily do this just like u said,without needing using subs command :

Download answer.mw

@Mathematix u want the answer to the third question ?! but the problem are not the same.since u have written exp(-3) but it is exp(-3*x) . your answer seems to be somewhat simpler but for more skillful member i think.
but both are doing the same thing.

if you write it in this way,(exp(-3*x)) u can easily do this just like u said,without needing using subs command :

Download answer.mws

these variables are function of times , when i use a[1](0.0001) it means a[1] for the time t=0.0001:

i need to have them as a function of time , so i can not remove (i+h=0.0001).i even use subs to substitute a[i](t)=b[i] but it does not solve the problem, i really do not know what should i do ?!

and as far as i know, {seq(expr,k=1..18)} = {seq}(expr,k=1..18) . am i wrong?

these variables are function of times , when i use a[1](0.0001) it means a[1] for the time t=0.0001:

i need to have them as a function of time , so i can not remove (i+h=0.0001).i even use subs to substitute a[i](t)=b[i] but it does not solve the problem, i really do not know what should i do ?!

and as far as i know, {seq(expr,k=1..18)} = {seq}(expr,k=1..18) . am i wrong?

@Carl Love perfect,really nice.

can i have the answer of the desolve after the singular ponit ? so that i can find what happens in the singular point? and also can i know number of singular points ?

can i have the answer of the desolve after the singular ponit ? so that i can find what happens in the singular point? and also can i know number of singular points ?

what is the relation governing to P(i)s? if u say the relation,i think it is to easy to find the sum .