document.write( "Question 442935: Solve the system:
\n" ); document.write( " $\"3x-y%2B2z=3\"$
\n" ); document.write( " $\"2x%2B3y-z=-3\"$
\n" ); document.write( " $\"x-2y%2B3z=2\"$ \r
\n" ); document.write( "\n" ); document.write( "Thanks :) \n" ); document.write( "

Algebra.Com's Answer #305526 by swincher4391(1107) $\"\"$ $\"About$

You can put this solution on YOUR website!
We will start by making an augmented matrix.\r
\n" ); document.write( "\n" ); document.write( " $\"matrix%283%2C4%2C3%2C-1%2C2%2C3%2C2%2C3%2C-1%2C-3%2C1%2C-2%2C3%2C2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Let's switch some rows so that we can get leading ones.\r
\n" ); document.write( "\n" ); document.write( " $\"matrix%283%2C4%2C1%2C-2%2C3%2C2%2C3%2C-1%2C2%2C3%2C2%2C3%2C-1%2C-3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Multiply row 2 and row 3 by -1.\r
\n" ); document.write( "\n" ); document.write( " $\"matrix%283%2C4%2C1%2C-2%2C3%2C2%2C-3%2C1%2C-2%2C-3%2C-2%2C-3%2C1%2C3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Notice we have leading ones now.\r
\n" ); document.write( "\n" ); document.write( "

\r
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\n" ); document.write( "\n" ); document.write( "Multiply row 1 by 3 and add it to row 2\r
\n" ); document.write( "\n" ); document.write( " $\"matrix%283%2C4%2C1%2C-2%2C3%2C2%2C0%2C-5%2C7%2C3%2C-2%2C-3%2C1%2C3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Multiply row 1 by 2 and add it to row 3\r
\n" ); document.write( "\n" ); document.write( " $\"matrix%283%2C4%2C1%2C-2%2C3%2C2%2C0%2C-5%2C7%2C3%2C0%2C-7%2C7%2C7%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Multiply row 3 by -1 and add it to row 2\r
\n" ); document.write( "\n" ); document.write( " $\"matrix%283%2C4%2C1%2C-2%2C3%2C2%2C0%2C2%2C0%2C-4%2C0%2C-7%2C7%2C7%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Divide row 2 by 2, and row 3 by 7.\r
\n" ); document.write( "\n" ); document.write( " $\"matrix%283%2C4%2C1%2C-2%2C3%2C2%2C0%2C1%2C0%2C-2%2C0%2C-1%2C1%2C1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Multiply row 2 by 2 add it to row 1 ... also add row 2 to row 3.\r
\n" ); document.write( "\n" ); document.write( " $\"matrix%283%2C4%2C1%2C0%2C3%2C-2%2C0%2C1%2C0%2C-2%2C0%2C0%2C1%2C-1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Multiply row 3 by -3 and add it to row 1.\r
\n" ); document.write( "\n" ); document.write( " $\"matrix%283%2C4%2C1%2C0%2C0%2C1%2C0%2C1%2C0%2C-2%2C0%2C0%2C1%2C-1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "x = 1, y = -2, z = -1.\r
\n" ); document.write( "\n" ); document.write( "Let's check:\r
\n" ); document.write( "\n" ); document.write( "3x + -y + 2z = 3(1) +2 -2 = 3
\n" ); document.write( "2x + 3y -z = 2(1) +3(-2) -(-1) = 2 -6 +1 = -3
\n" ); document.write( "x - 2y + 3z = 1 +4 -3 = 2\r
\n" ); document.write( "\n" ); document.write( "So yes, the solution works.
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