document.write( "Question 940697: Solve the following systems of equations using Cramer Rule. [10 marks]
\n" );
document.write( "X+Y+Z=2
\n" );
document.write( "Z+2Y+X=1
\n" );
document.write( "Y+4X+2Z=0 \n" );
document.write( "
Algebra.Com's Answer #573316 by krutarthas(22)![]() ![]() You can put this solution on YOUR website! x + y + z = 2 -----(1) \n" ); document.write( "x + 2y + z = 1 -----(2) \n" ); document.write( "4x +y+2z = 0 -----(3)\r \n" ); document.write( "\n" ); document.write( "Δ = \n" ); document.write( " | 1 1 1 | \n" ); document.write( " | 1 2 1 | \n" ); document.write( " | 4 1 2 |\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "= 1(4 - 1) – 1(2 - 4) + 1(1 - 8) \n" ); document.write( "= 3+2-7 \n" ); document.write( "= -2 \n" ); document.write( "Here Determinant is not equal to zero, Hence Cramer’s rule can be applicable. \n" ); document.write( "X = ∆x / ∆ , y = ∆y / ∆ , z = ∆z / ∆ \n" ); document.write( "Δx = \n" ); document.write( " | 2 1 1 | \n" ); document.write( " | 1 2 1 | \n" ); document.write( " | 0 1 2 |\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "=2(4-1)-1(2-0)+1(1-0) \n" ); document.write( "=6-2+1 \n" ); document.write( "∆x= 5\r \n" ); document.write( "\n" ); document.write( "Δy = \n" ); document.write( " | 1 2 1 | \n" ); document.write( " | 1 1 1 | \n" ); document.write( " | 4 0 2 |\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "= 1(2-0)-2(2-4)+1(0-4 ) \n" ); document.write( "=2+4-4 \n" ); document.write( "∆y= 2 \n" ); document.write( "Δz = \n" ); document.write( " | 1 1 2 | \n" ); document.write( " | 1 2 1 | \n" ); document.write( " | 4 1 0 |\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "= 1(0-1)-1(0-4)+2(1-8) \n" ); document.write( "= -1+4-14 \n" ); document.write( "∆z= -11\r \n" ); document.write( "\n" ); document.write( "By using Cramer’s rule: \n" ); document.write( "x = Δx / ∆ \n" ); document.write( "x = 5/-2 \n" ); document.write( "x = -2.5 \n" ); document.write( "y = Δy / ∆ \n" ); document.write( "y = 2 / -2 \n" ); document.write( "y = -1 \n" ); document.write( "z = Δz / ∆ \n" ); document.write( "z = -11/-2 \n" ); document.write( "z = 5.5 \n" ); document.write( "Therefore the required x = -2.5, y = -1 & z = 5.5\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |