# Math Help - solve simultaneous equations by matrix

1. ## solve simultaneous equations by matrix

I have 4 simultaneous equations as below

$

\begin{array}{l}
2I_1 + 2 - 1000I_3 = 0 \\
1000I_3 - 3000I_4 - 10 = 0 \\
0.003 - I_1 - I_2 = 0 \\
I_2 - I_3 - I_4 = 0 \\
\end{array}

$

I understand as far as putting them in matrix vector form, as below.
$

\left[ {\begin{array}{*{20}c}
{2000} & 0 & { - 1000} & 0 \\
0 & 0 & {1000} & { - 3000} \\
1 & 1 & 0 & 0 \\
0 & 1 & { - 1} & { - 1} \\
\end{array}} \right]\left[ {\begin{array}{*{20}c}
{I_1 } \\
{I_2 } \\
{I_3 } \\
{I_4 } \\
\end{array}} \right] = \left[ {\begin{array}{*{20}c}
{ - 2} \\
{10} \\
{0.003} \\
0 \\
\end{array}} \right]

$

However I do not understand how to solve. Does it have to be put in echelon form, if so how is it done I get loss with doing that. Could some please try and explain it to me. Unfortunately you will probably have to dumb is right down for me. Thankyou.

2. I think what you have to do is find the inverse of the 4x4 matrix on the left and then multiply both sides on the left by this inverse. Then you will have a matrix with I's on the left and when you multiply out the right hand side you will have a matrix with only numbers. so I1 = the first element and so on.

3. ## by cramer rule

find I1=D1/D
I2=D2/D
I3=D3/D
I4=D4/D

The cramer rule.
It is something trivial or non trivial. Or singular and non singular one.

4. How do I find the inverse matrix, could someone please do some of the working so I can try and follow.

Thankyou.