document.write( "Question 827186: I Want to know the solution.
\n" ); document.write( "solve by Cramer's Rule, equations are
\n" ); document.write( "2x-2y+3z=0
\n" ); document.write( "x+y+z=0
\n" ); document.write( "x+3y+z=0
\n" ); document.write( "of 3X3 Matrix \n" ); document.write( "
Algebra.Com's Answer #498574 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
let A be the 3 by 3 matrix
\n" ); document.write( "| a b c |
\n" ); document.write( "| d e f |
\n" ); document.write( "| g h i |
\n" ); document.write( "then the determinant of A is written |A| = D and
\n" ); document.write( "D = a(ei-fh) -b(di-fg) +c(dh-eg)
\n" ); document.write( "we are given a system of linear equations whose 3 by 3 coefficient matrix is the following and the solution column is three 0's
\n" ); document.write( "| 2 -2 3|
\n" ); document.write( "| 1 1 1|
\n" ); document.write( "| 1 3 1|
\n" ); document.write( "let's calculate the determinant of the coefficient matrix
\n" ); document.write( "D = 2(1-3) -(-2)(1-1) +3(3-1) = 2
\n" ); document.write( "now the determinant for x is calculated from the coefficient matrix with the x column replaced with the solution column
\n" ); document.write( "| 0 -2 3|
\n" ); document.write( "| 0 1 1|
\n" ); document.write( "| 0 3 1|
\n" ); document.write( "Dx = 0 -(-2)(0-0) +3(0-0) = 0
\n" ); document.write( "now the determinant for y is calculated from the coefficient matrix with the y column replaced with the solution column
\n" ); document.write( "| 2 0 3|
\n" ); document.write( "| 1 0 1|
\n" ); document.write( "| 1 0 1|
\n" ); document.write( "Dy = 2(0-0) - 0(1-1) +3(0-0) = 0
\n" ); document.write( "now the determinant for z is calculated from the coefficient matrix with the z column replaced with the solution column
\n" ); document.write( "| 2 -2 0|
\n" ); document.write( "| 1 1 0|
\n" ); document.write( "| 1 3 0|
\n" ); document.write( "Dz = 2(0-0) -(-2)(0-0) +0(3-1) = 0
\n" ); document.write( "now Cramer's rule tells us that x = Dx/D, y = Dy/D, z = Dz/D, therefore
\n" ); document.write( "x = 0/2 = 0
\n" ); document.write( "y = 0/2 = 0
\n" ); document.write( "z = 0/2 = 0\r
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