document.write( "Question 167138This question is from textbook
\n" ); document.write( ": can someone please show me how to do this problem:\r
\n" ); document.write( "\n" ); document.write( "Find the inverse, if it exists, of the given matrix\r
\n" ); document.write( "\n" ); document.write( "[2 -1 0]
\n" ); document.write( "[3 -2 0]
\n" ); document.write( "[-2 3 1]\r
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\n" ); document.write( "\n" ); document.write( "a.
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\n" ); document.write( "[3 -2 0]
\n" ); document.write( "[-5 4 -1]\r
\n" ); document.write( "\n" ); document.write( "b.
\n" ); document.write( "[1 -1 0]
\n" ); document.write( "[3 -2 1]
\n" ); document.write( "[-5 4 -1]\r
\n" ); document.write( "\n" ); document.write( "c.
\n" ); document.write( "[2 -1 0]
\n" ); document.write( "[3 2 0]
\n" ); document.write( "[-5 4 1]\r
\n" ); document.write( "\n" ); document.write( "d.
\n" ); document.write( "[2 -1 0]
\n" ); document.write( "[3 -2 0]
\n" ); document.write( "[-5 4 1]
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Algebra.Com's Answer #123109 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Augment it with the identity matrix:\r\n" );
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document.write( "Now do row operations to get the identity on the left\r\n" );
document.write( "of the partition and then the inverse will be on the right\r\n" );
document.write( "of the partition.  We will place all the 0's first,\r\n" );
document.write( "then we will place the 1's.\r\n" );
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document.write( "To get a 0 where the 3 in the 2nd row is, \r\n" );
document.write( "multiply the 1st row by -3\r\n" );
document.write( "multiply the second row by 2\r\n" );
document.write( "Add -3 times the 1st row to 2 times the 2nd row\r\n" );
document.write( "Keep the 1st row as it is.\r\n" );
document.write( "This work can be done mentally if you will write -3\r\n" );
document.write( "to the left of the 1st row and 2 to the left of the\r\n" );
document.write( "2nd row.  Then fill in the next matrix with a new 2nd\r\n" );
document.write( "row.  The other two rows will remain the same.\r\n" );
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document.write( "To get a 0 where the -2 in the 3rd row is, \r\n" );
document.write( "multiply the 1st row by 1 (leave it as it is)\r\n" );
document.write( "multiply the second row by 1 (leave it as it is)\r\n" );
document.write( "Add 1 times the 1st row to 1 times the 3rd row\r\n" );
document.write( "Keep the 1st row as it is.\r\n" );
document.write( "This work can be done mentally easily if you'll\r\n" );
document.write( "put 1's left of the 1st and 3rd rows.\r\n" );
document.write( "Then fill in the next matrix with a new 3rd\r\n" );
document.write( "row.   The other two rows will remain the same.\r\n" );
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document.write( "To get a 0 where the -1 in the 1st row is, \r\n" );
document.write( "multiply the 2nd row by -1\r\n" );
document.write( "multiply the 1st row by 1 (leave it as it is)\r\n" );
document.write( "Add -1 times the 2nd row to 1 times the 1st row\r\n" );
document.write( "Keep the 2nd row as it is.\r\n" );
document.write( "This work can be done mentally if you will write -1\r\n" );
document.write( "to the left of the 2nd row and 1 to the left of the\r\n" );
document.write( "1st row.  Then fill in the next matrix with a new 1st\r\n" );
document.write( "row. The other two rows will remain the same.\r\n" );
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document.write( "To get a 0 where the 2 in the 3rd row is, \r\n" );
document.write( "multiply the 2nd row by 2\r\n" );
document.write( "multiply the 3rd row by 1 (leave it as it is)\r\n" );
document.write( "Add 2 times the 2nd row to 1 times the 3rd row\r\n" );
document.write( "Keep the 2nd row as it is.\r\n" );
document.write( "This work can be done mentally if you will write 2\r\n" );
document.write( "to the left of the 2nd row and 1 to the left of the\r\n" );
document.write( "3rd row.  Then fill in the next matrix with a new 3rd\r\n" );
document.write( "row. The other two rows will remain the same.\r\n" );
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document.write( "Now we have all the 0's placed. We need to get a 1 where \r\n" );
document.write( "the 2 in in the 1st row.  To do that we multiply the 1st\r\n" );
document.write( "row through by . Or you can think of it as \r\n" );
document.write( "dividing the row through by 2:\r\n" );
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document.write( "We need to get a 1 where \r\n" );
document.write( "the -1 in in the 2nd row.  To do that we multiply the 2nd\r\n" );
document.write( "row through by . Or you can think of it as \r\n" );
document.write( "changing all the signs in the 2nd row:\r\n" );
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document.write( "The inverse of the original matrix is found right of \r\n" );
document.write( "the partition.  So the answer is\r\n" );
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document.write( ", choice d.\r\n" );
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document.write( "Edwin

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