\

- Steve

Sure can!  With matlab of course.

You have a matrix A, vector X and solution vector b.
So you have A * X = b and you wanna know the vector X.
So in matlab, you fill in the matrix with your coefficients, then type on the following line B = inv(A);  This will inverse your matrix.
Then compute B*b';  (dont forget to put a ' behind the b, it indicates you take the transpose of your vector b so the rowvector becomes a columnvector)
The solution will be a vector with your solution, from x1 to x20 in order.

Nah, try this

>> help \

or more verbosely

>> help mldivide

Computing the inverses of large matrices is pretty expensive.

- Steve

The attached data sheet is very typical ; because a*x does not equal to b in real practical scenario ;

actually, this b answer is nothing but we can say a1x1+b1x2+c1x3+.....+t1x20 = b ;where b is known,  a1,b1,...t20 is known but x1,x2 ,x3 are not known. like that equation is there.

similary , a2x1+b2x2+c2x3+.......+t2x20 = c ; where c is known, a2,x2...t2 are known but x1,x2,x3 ....are not known which is same as in section 1. basically, a1,a2...etc. are stream composition which is known through laboratery while x1,x2...x20 are 20 different streams flow is not known which is to be find out,ultimately all 20 streams mix to the main stream where composition and total flow is known that is why b,c..on right side is known. like this way.as attached in sheet.
 

You have a system of linear equations as explained here:

http://en.wikipedia.org/wiki/System_of_linear_equations

Note how the "General Form" matches your problem statement.

- Steve

yes..u r right steve.

While running Matlab,some of the X1,X2 values out of 20 sterams are coming negative which is practically not possible as these are all flow rates of streams , how to correct in Matlab , is there any provisition in Matlab so, that we can have postiive coefficient and not negative ?

You'd need to study the Matlab help docs for options that can be used

http://www.mathworks.com/access/helpdesk/help/techdoc/ref/linsolve.html

You may find something in there that's useful.  Alternatively, ask some of the specialists in the comp.soft-sys.matlab newsgroup.  There are many people well versed in linear equations and their nuances.

- Steve