[?] Calculate matrix constants given all values for the matrices variables?

Questions
1

I have a matrix G, H, and J

G.PNG
G.PNG856×299 5.73 KB

HJ.PNG
HJ.PNG628×567 6.25 KB

I have given all the values for the varibales given in the matrices

I want to calculate for H matrix constants.

k = MatrixForm[
  Solve[{G.H == J}, {Subscript[C, 1], Subscript[C, 2], Subscript[C, 
    4], Subscript[C, 5], Subscript[C, 6], Subscript[C, 7], Subscript[
    C, 10], Subscript[C, 11]}]]

Output:

(Subscript[C, 1]->0. -0.0000809814 P+0.0043219 V	Subscript[C, 2]->3.83204*10^-9 P-7.80102*10^-7 V	Subscript[C, 4]->2.24561*10^-8 P-4.02257*10^-6 V	Subscript[C, 5]->4.65722*10^-10 P-1.10168*10^-7 V	Subscript[C, 6]->-4.20314*10^-14 P+9.94267*10^-12 V	Subscript[C, 7]->-0.0000161671 P-0.00309882 V	Subscript[C, 10]->9.15123*10^-10 P+2.10854*10^-7 V	Subscript[C, 11]->-9.43931*10^-10 P+7.89909*10^-8 V)

If I have to use the constant C1 in other expression, what command should I use? If I use simply C1 it is not considering the numerical value from it. It takes the element as C1.

2

Remove the MatrixForm from the definition of k:

k = 
  First@Solve[{G.H == J}, {Subscript[C, 1], Subscript[C, 2], Subscript[C, 
    4], Subscript[C, 5], Subscript[C, 6], Subscript[C, 7], Subscript[
    C, 10], Subscript[C, 11]}]

Then you extract the value of Subscript[C, 1] with

Subscript[C, 1]/.k

Look up how to use the output of Solve, which is not intuitive at all.

3

Thank you very much.

It worked perfectly. I will read further about Solve commands.

Regards,
Gowtham

4

Could you let me know why I get this error?

RowReduce::luc: Result for RowReduce of badly conditioned matrix {{0.,0.,0.,0.,0.,1.,-4.65646,0.00009025,0.},{0.,0.,0.,0.,0.,0.,105.263,0.019,0.},<<4>>,{-2708.16,0.,0.920204,0.,0.,0.,655.536,-0.11989,0.04095},{5.61087*10^7,0.,-5416.31,4.01349*10^11,-3.67011*10^7,0.,0.,0.,-292.5}} may contain significant numerical errors.
5

Perhaps your matrix G is badly conditioned numerically. Can you give exact values to the entries?

6

That is not possible to give exact values since all those variables are calculated from other different equations.

7

Mathematica should give an estimate of the significant digits of the results. If that is not enough for you, you can try to increase the precision first in solving the differential equations.