Question 1084344
.
About Cramer's rule read 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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/The-trick-to-solve-some-word-problems-with-three-and-more-unknowns.lesson>The tricks to solve some word problems with three and more unknowns using mental math</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-systems-of-non-linear-equations-in-three-unknowns-using-Cramer%27s-rule.lesson>Solving systems of non-linear equations in three unknowns using Cramer's rule</A>

in this site.



Now let me reveal you one secret.


For matrices of dimensions 4, 5 and higher, practically nobody in nova days applies Cramer's rule with handle/manual calculations. 
People use calculators or computer software. Very popular are internet sites that offer online solutions (solvers) for free . . . (!)


One such solver you can find at the link 
<A HREF=http://matrix.reshish.com/cramSolution.php>http://matrix.reshish.com/cramSolution.php</A>


http://matrix.reshish.com/cramSolution.php



I used it to get the solution presented below:


<pre>
Your matrix

&#8470;	X1	X2	X3	X4	X5	b
1	2	4	4	3	8	3
2	7	10	10	5	2	5
3	1	6	8	7	5	7
4	5	5	4	10	5	10
5	5	1	7	6	3	6

Write down the main matrix and find its determinant

&#8470;	X1	X2	X3	X4	X5
1	2	4	4	3	8
2	7	10	10	5	2
3	1	6	8	7	5
4	5	5	4	10	5
5	5	1	7	6	3
D = -16605

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

&#8470;	X1	X2	X3	X4	X5
1	3	4	4	3	8
2	5	10	10	5	2
3	7	6	8	7	5
4	10	5	4	10	5
5	6	1	7	6	3
D1 = 0

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

&#8470;	X1	X2	X3	X4	X5
1	2	3	4	3	8
2	7	5	10	5	2
3	1	7	8	7	5
4	5	10	4	10	5
5	5	6	7	6	3
D2 = 0

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

&#8470;	X1	X2	X3	X4	X5
1	2	4	3	3	8
2	7	10	5	5	2
3	1	6	7	7	5
4	5	5	10	10	5
5	5	1	6	6	3
D3 = 0

Replace the 4th column of the main matrix with the solution vector and find its determinant

&#8470;	X1	X2	X3	X4	X5
1	2	4	4	3	8
2	7	10	10	5	2
3	1	6	8	7	5
4	5	5	4	10	5
5	5	1	7	6	3
D4 = -16605

Replace the 5th column of the main matrix with the solution vector and find its determinant

&#8470;	X1	X2	X3	X4	X5
1	2	4	4	3	3
2	7	10	10	5	5
3	1	6	8	7	7
4	5	5	4	10	10
5	5	1	7	6	6
D5 = 0

x1 = D1 / D = 0 / (-16605) = 0
x2 = D2 / D = 0 / (-16605) = 0
x3 = D3 / D = 0 / (-16605) = 0
x4 = D4 / D = (-16605) / (-16605) = 1
x5 = D5 / D = 0 / (-16605) = 0

Solution set:

x1 = 0
x2 = 0
x3 = 0
x4 = 1
x5 = 0
</pre>