document.write( "Question 171695: I don't understand the steps of the Matrix for these equations. Could you please show me?\r
\n" ); document.write( "\n" ); document.write( "7x+8y-z=9
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Algebra.Com's Answer #126829 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Put 1's in front of the single letters\r\n" );
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document.write( "Separate into terms, erasing the plus signs, keeping\r\n" );
document.write( "the minus signs as negative signs:\r\n" );
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document.write( "Erase all the letters and replace the equal signs\r\n" );
document.write( "with \"|\"'s:\r\n" );
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document.write( "Erase the brace and put parentheses around it:\r\n" );
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document.write( "Now we want to end up with a matrix like this,\r\n" );
document.write( "with three zeros on the the bottom left, and\r\n" );
document.write( "numbers everywhere else:\r\n" );
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document.write( "Start with this:\r\n" );
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document.write( "Swap the rows so that the smallest number in absolute\r\n" );
document.write( "value in the first column is on the far left of the \r\n" );
document.write( "top row.  Since 1 is the smallest number in absolute\r\n" );
document.write( "value in row 1, I will swap rows 1 and 2:\r\n" );
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document.write( "Now we will add -7 times the top row to the 2nd row,\r\n" );
document.write( "to get a zero where the 7 is. It's easier if you\r\n" );
document.write( "write -7 to the left of the top row and 1 to the left\r\n" );
document.write( "of the second row,and write that equal to a new matrix\r\n" );
document.write( "with the same 1st and 3rd rows, with a blank middle row:\r\n" );
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document.write( "Then you can easily fill in the blank row term by term as:\r\n" );
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document.write( "Since all the numbers in the middle row are even, we can\r\n" );
document.write( "multiply it through by :\r\n" );
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document.write( "Now we will add 7 times the top row to the 3rd row,\r\n" );
document.write( "to get a zero where the -7 is. It's easier if you\r\n" );
document.write( "write 7 to the left of the top row and 1 to the left\r\n" );
document.write( "of the bottom row,and write that equal to a new matrix\r\n" );
document.write( "with the same 1st and 2nd rows, with a blank bottom row:\r\n" );
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document.write( "Then you can easily fill in the blank row term by term as:\r\n" );
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document.write( "---\r\n" );
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document.write( "Now we will add 13 times the middle row to 11 times\r\n" );
document.write( "the 3rd row, to get a zero where the -13 is. It's \r\n" );
document.write( "easier if you write 13 to the left of the middle row \r\n" );
document.write( "and 11 to the left of the bottom row,and write that \r\n" );
document.write( "equal to a new matrix with the same 1st and 2nd rows,\r\n" );
document.write( "with a blank bottom row:\r\n" );
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document.write( "Then you can easily fill in the blank row term by term as:\r\n" );
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document.write( "The bottom row can be multiplied through by \r\n" );
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document.write( "Now we put the letters back as we took them out, and\r\n" );
document.write( "put equal signs where the \"|\"'s are:\r\n" );
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document.write( "So we have this system:\r\n" );
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document.write( "Now we do what is called \"back-substitution\":\r\n" );
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document.write( "Substitute  into the middle equation:\r\n" );
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document.write( "Finally substitute both  and  in\r\n" );
document.write( "the top equation:\r\n" );
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document.write( "So , , .\r\n" );
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document.write( "Edwin

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