document.write( "Question 824806: Solve the problem.
\n" ); document.write( "Given that | x y z | = 3, find the value of the determinant | 2 4 5 |
\n" ); document.write( "..................| a b c |.............................................................| 3a 3b 3c |
\n" ); document.write( "..................| 2 4 5 |.............................................................| x-2 y-4 z-5 |
\n" ); document.write( "(dots are just to line problems up)(hope that makes sense) \n" ); document.write( "

Algebra.Com's Answer #496824 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "FIRST DETERMINANT = ,  SECOND DETERMINANT = \r\n" );
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document.write( "We notice that \r\n" );
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document.write( "1. the second determinant's top row is the same as\r\n" );
document.write( "the first matrix's bottom row. \r\n" );
document.write( "2. we notice that the second determinant's middle row is \r\n" );
document.write( "the first determinant's middle row multiplied by 3.\r\n" );
document.write( "3. we notice that the second determinant's bottom row is\r\n" );
document.write( "the first determinant's top row with the first determinant's\r\n" );
document.write( "bottom row subtracted from it.\r\n" );
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document.write( "So let's start with the first determinant \r\n" );
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document.write( "and do row operations until we get the second determinant.  \r\n" );
document.write( "Let's begin by swapping the top and bottom rows:\r\n" );
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document.write( "We remember the rule that when we swap two rows in a determinant,\r\n" );
document.write( "we multiply the value of the determinant by -1, so\r\n" );
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document.write( "We notice that the second determinant's middle row is this\r\n" );
document.write( "determinant's middle row multiplied by 3.  So we multiply\r\n" );
document.write( "this determinant's middle row by 3.\r\n" );
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document.write( "We remember the rule that when we multiply a row in a determinant\r\n" );
document.write( "by a scalar (constant), we multiply the value of the determinant \r\n" );
document.write( "by that same constant, so the value of the determinant is multiplied \r\n" );
document.write( "by 3:\r\n" );
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document.write( "Finally we notice that the second determinant's bottom row is\r\n" );
document.write( "this determinant's bottom row with the top row subtracted from it\r\n" );
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document.write( "We remember the rule that if we add a multiple of one row to \r\n" );
document.write( "another row, we do not change the value of the determinant, so\r\n" );
document.write( "we add -1 times the top row from the bottom row and we will\r\n" );
document.write( "not change the value of the determinant, so we have:\r\n" );
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document.write( "Edwin

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