Maple don't solve equations

I am trying to solve these equations:

S := solve({ PVA1+PSA1+PPA1=1, 开发者_如何转开发 PVA2+PSA2+PPA2=1, PVA3+PSA3+PPA3=1, PVA1*0.2+PVA2*0.5+PVA3*0.3=0.3, PSA1*0.2+PSA2*0.5+PSA3*0.3=0.2, PPA1*0.2+PPA2*0.5+PPA3*0.3=0.3}, Explicit=true) ;

But maple gives S := NULL. Any ideas? PS equations have some solutions.

The linear system as you have posted it is inconsistent. You can check this out for yourself by writing:

with(LinearAlgebra):

eqns := [PVA1+PSA1+PPA1=1, PVA2+PSA2+PPA2=1, PVA3+PSA3+PPA3=1, PVA1*0.2+PVA2*0.5+PVA3*0.3=0.3, PSA1*0.2+PSA2*0.5+PSA3*0.3=0.2, PPA1*0.2+PPA2*0.5+PPA3*0.3=0.3]:

M := GenerateMatrix(eqns, indets(eqns), augmented=true):

LinearSolve(M);

Error, (in LinearAlgebra:-LA_Main:-BackwardSubstitute) inconsistent system

To see exactly why it is inconsistent look at the last row resulting from

ReducedRowEchelonForm(M);