![\"\"](\"/images/stars/stars-12.gif\")
You can put this solution on YOUR website!
This is identical to problem 20131. Here it is again:\r
\n" ); document.write( "\n" ); document.write( "Complex_Numbers/20131: Linear Systems
\n" ); document.write( "w+2x+3y-4z=-5
\n" ); document.write( "2w-x+y-2z=-7
\n" ); document.write( "3w-x-2y+z=7
\n" ); document.write( "4w-4x-2y+3z=3\r
\n" ); document.write( "\n" ); document.write( "1 solutions\r
\n" ); document.write( "\n" ); document.write( "--------------------------------------------------------------------------------
\n" ); document.write( "Answer 9718 by AnlytcPhil(150) on 2005-11-19 10:38:59 (Show Source): \r
\n" ); document.write( "\n" ); document.write( "w + 2x + 3y - 4z = -5
\n" ); document.write( "2w - x + y - 2z = -7
\n" ); document.write( "3w - x - 2y + z = 7
\n" ); document.write( "4w - 4x - 2y + 3z = 3
\n" ); document.write( "`
\n" ); document.write( "Get it in row echelon form. That is, this form:
\n" ); document.write( "`
\n" ); document.write( " w + 2x + 3y - 4z = -5
\n" ); document.write( " Ax + By + Cz = D
\n" ); document.write( " Ey + Fz = G
\n" ); document.write( " Hz = I
\n" ); document.write( "`
\n" ); document.write( " w + 2x + 3y - 4z = -5
\n" ); document.write( "2w - x + y - 2z = -7
\n" ); document.write( "3w - x - 2y + z = 7
\n" ); document.write( "4w - 4x - 2y + 3z = 3
\n" ); document.write( "`
\n" ); document.write( "Get rid of the 2w by adding -2 times the first equation
\n" ); document.write( "to it, and replacing it by what you get
\n" ); document.write( "`
\n" ); document.write( " w + 2x + 3y - 4z = -5
\n" ); document.write( " - 5x - 5y + 6z = 3
\n" ); document.write( "3w - x - 2y + z = 7
\n" ); document.write( "4w - 4x - 2y + 3z = 3
\n" ); document.write( "`
\n" ); document.write( "Get rid of the 3w by adding -3 times the first equation
\n" ); document.write( "to it, and replacing it by what you get
\n" ); document.write( "`
\n" ); document.write( " w + 2x + 3y - 4z = -5
\n" ); document.write( " - 5x - 5y + 6z = 3
\n" ); document.write( " - 7x - 11y + 13z = 22
\n" ); document.write( "4w - 4x - 2y + 3z = 3
\n" ); document.write( "`
\n" ); document.write( "Get rid of the 4w by adding -4 times the first equation
\n" ); document.write( "to it, and replacing it by what you get
\n" ); document.write( "`
\n" ); document.write( " w + 2x + 3y - 4z = -5
\n" ); document.write( " -5x - 5y + 6z = 3
\n" ); document.write( " -7x - 11y + 13z = 22
\n" ); document.write( " -12x - 14y + 19z = 23
\n" ); document.write( "`
\n" ); document.write( "Get rid of the -7x by adding -7 times the second equation, or
\n" ); document.write( "35x + 35y - 42z = -21, to 5 times the third equation, which is
\n" ); document.write( "-35x - 55y + 65z = 110, getting -20y + 23z = 89, and replacing
\n" ); document.write( "the third equation by it.
\n" ); document.write( "`
\n" ); document.write( " w + 2x + 3y - 4z = -5
\n" ); document.write( " -5x - 5y + 6z = 3
\n" ); document.write( " -20y + 23z = 89
\n" ); document.write( " -12x - 14y + 19z = 23
\n" ); document.write( "`
\n" ); document.write( "Get rid of the -12x by adding -12 times the second equation, or
\n" ); document.write( "60x + 60y - 72z = -36 to 5 times the fourthion, which is
\n" ); document.write( "-60x - 70y + 95z = 115, getting -10y + 23z = 79, and replacing the
\n" ); document.write( "third equation by it
\n" ); document.write( "`
\n" ); document.write( " w + 2x + 3y - 4z = -5
\n" ); document.write( " -5x - 5y + 6z = 3
\n" ); document.write( " -20y + 23z = 89
\n" ); document.write( " -10y + 23z = 79
\n" ); document.write( "`
\n" ); document.write( "Get rid of the -10y by adding -1 times the third equation, which is
\n" ); document.write( "20y - 23z = -89 to 2 times the fourth equation, which is
\n" ); document.write( "-20y + 46z = 158, getting 23z = 69, and replacing the third equation
\n" ); document.write( "by it.
\n" ); document.write( "`
\n" ); document.write( " w + 2x + 3y - 4z = -5
\n" ); document.write( " -5x - 5y + 6z = 3
\n" ); document.write( " -20y + 23z = 89
\n" ); document.write( " 23z = 69
\n" ); document.write( "`
\n" ); document.write( "To finish,
\n" ); document.write( "(1) Solve the 4th equation for z,
\n" ); document.write( "(2) Substitute this value of z into the 3rd equation and solve for y
\n" ); document.write( "(3) Substitute the values for x and y into the 2nd equation and solve for x
\n" ); document.write( "(4) Substitute the values for z, y, and x in the 1st equation to find w.
\n" ); document.write( "Answer (w, x, y, z) = (2, 4, -1, 3)
\n" ); document.write( "`
\n" ); document.write( "Edwin McCravy
\n" ); document.write( "AnlytcPhil@aol.com
\n" ); document.write( " \n" ); document.write( "