Question 1179371
.
Consider the circuit in the figure. The currents I1, I2, and I3 in amperes are given by the solution of the system of linear equations.
4I1 + 8I3 = 18
2I2 + 8I3 = 54
I1 + I2 − I3 = 0
Use Cramer's Rule to find the three currents.
I1 =
I2 =
I3 =
~~~~~~~~~~~~~~~~~~~


<pre>
Your matrix

        X1	X2	X3	b
1	4	0	8	18
2	0	2	8	54
3	1	1	-1	0


Write down the main matrix and find its determinant

        X1	X2	X3
1	4	0	8
2	0	2	8
3	1	1	-1

Δ = -56


Replace the 1st column of the main matrix with the solution vector and find its determinant

        X1	X2	X3
1	18	0	8
2	54	2	8
3	0	1	-1

Δ1 = 252


Replace the 2nd column of the main matrix with the solution vector and find its determinant

        X1	X2	X3
1	4	18	8
2	0	54	8
3	1	0	-1

Δ2 = -504


Replace the 3rd column of the main matrix with the solution vector and find its determinant

        X1	X2	X3
1	4	0	18
2	0	2	54
3	1	1	0

Δ3 = -252


x1 = Δ1 / Δ = 252 / (-56) = -9/2
x2 = Δ2 / Δ = (-504) / (-56) = 9
x3 = Δ3 / Δ = (-252) / (-56) = 9/2


Solution set:

x1 = -9/2
x2 = 9
x3 = 9/2
</pre>


Solved.


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On Cramer's rule for solving systems of 3 equations in 3 unknowns see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Determinant-of-a-3x3-matrix.lesson>Determinant of a 3x3 matrix</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Co-factoring-a-3x3-determinant.lesson>Co-factoring the determinant of a 3x3 matrix</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/HOW-TO-solve-system-of-linear-eqns-in-three-unknowns-using-det.lesson>HOW TO solve system of linear equations in three unknowns using determinant (Cramer's rule)</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-systems-of-linear-equations-in-three-unknowns-using-determinant.lesson>Solving systems of linear equations in three unknowns using determinant (Cramer's rule)</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-word-problems-by-reducing-them-to-systems-of-linear-equations-in-three-unknowns.lesson>Solving word problems by reducing to systems of linear equations in three unknowns</A>

in this site.



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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic 
&nbsp;&nbsp;&nbsp;&nbsp; "<U>3x3-Matrices, determinants, Cramer's rule for systems in three unknowns</U>" 



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