Practical? (Symbolic System of equations to be turned into a Matrix then inverted to gain solution)

I am looking to organize the  equation (E.1, E.2, E.3, E.4, E.5).. I have five unknowns (I.1, I.2, I.3, I.4, I.5)  and the five equations already mentioned (E.1, E.2, E.3, E.4, E.5).  I want to organize the equation  in terms of  some number = an equation defined but the unknowns. I.E. (19=28*I.1+70*I.2+99*I.3-7453*I.4-972364*I.5) I then want to extract the coefficients. The place the coefficient into a matrix one equations at time till i have square matrix i can solve for. (I.E. invert roe escholon etc. etc low lever linear algebra.. if the matrix is not invertible i can throw and error?) I understand what your doing buy looking at the equations and just copying the equations into a matrix then solving for it. I am petty. i might want to do a simulation of passive components then run a script and some mathcad commands to check my other math cad work. I was working for a trainer and maybe went over board looking to use symbolics.

I can see your getting a solution. I can see you putting an initial value into the variable of the imaginary number square root of negative one i believe. I have to explain to the tutor/ friend why i am doing this in mathcad and how it gets me the answer i need. So i go back to what i know linear algebra and i try to make mathcad conform to formula i know. Your time is money.. Do you have any books to suggest that might explain this as i am probably more easily confused and have to be thorough in my explanation to my tutor?  (Worse i could (Henry David) Thoreau in my work which might be too wordy and too nerdy.)