document.write( "Question 174894This question is from textbook saxon algebra 2
\n" ); document.write( ": Find the inverse of \"+matrix%281%2C3%2C+A%2C+%22=%22%2C+%28matrix%282%2C2%2C-3%2C1%2C-5%2C5%29%29++%29+\" if it exists. \n" ); document.write( "
Algebra.Com's Answer #130001 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
Find the inverse of A = \"%28matrix%282%2C2%2C-3%2C1%2C-5%2C5%29%29\" if it exists.
\n" ); document.write( "
\r\n" );
document.write( "Method 1:\r\n" );
document.write( "\r\n" );
document.write( "Start with the matrix:\r\n" );
document.write( "\"+matrix%281%2C3%2C+A%2C+%22=%22%2C+%28matrix%282%2C2%2C-3%2C1%2C-5%2C5%29%29++%29+\"\r\n" );
document.write( "\r\n" );
document.write( "Augment it on the right with the identity matrix, \"%28matrix%282%2C2%2C1%2C0%2C0%2C1%29%29%29\",\r\n" );
document.write( "like this\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "Now we do row operations to get the identity on the left:\r\n" );
document.write( "\r\n" );
document.write( "To get a zero where the -5 is,\r\n" );
document.write( "\r\n" );
document.write( "Add -5 times row 1 to 3 times row 2.  It's a good idea\r\n" );
document.write( "to write the number you're multiplying row by, on\r\n" );
document.write( "the far left:\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%282%2C1%2C-5%2C3%29\"\r\n" );
document.write( "\r\n" );
document.write( "The result is:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next we get a zero where the 1 is in row 1, column 2\r\n" );
document.write( "by adding 1 times row 2 to -10 times row 1.\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%282%2C1%2C-10%2C1%29\"\r\n" );
document.write( "\r\n" );
document.write( "The result is:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "Get a 1 where the 30 is by multiplying row 1\r\n" );
document.write( "by \"1%2F30\"\r\n" );
document.write( "\r\n" );
document.write( "Get a 1 where the 10 is by multiplying row 2\r\n" );
document.write( "by \"1%2F10\"\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%282%2C1%2C1%2F30%2C1%2F10%29\"\r\n" );
document.write( "\r\n" );
document.write( "The result is:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "So the inverse of \"A\" or \"A%5E%28-1%29\" is the part on the right:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That method works for all matrices.\r\n" );
document.write( "\r\n" );
document.write( "------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Here's a method that works only for 2x2 matrices:\r\n" );
document.write( "\r\n" );
document.write( "Method 2:\r\n" );
document.write( "\r\n" );
document.write( "Start with the matrix:\r\n" );
document.write( "\r\n" );
document.write( "\"%28matrix%282%2C2%2C-3%2C1%2C-5%2C5%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Find the determinant of the matrix:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Swap the upper left and lower right elements:\r\n" );
document.write( "\r\n" );
document.write( "\"%28matrix%282%2C2%2C5%2C1%2C-5%2C-3%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Change the signs of the upper right and lower left elements:\r\n" );
document.write( "\r\n" );
document.write( "\"%28matrix%282%2C2%2C5%2C-1%2C5%2C-3%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Divide every element by the -10 which was the determinant of the\r\n" );
document.write( "original matrix:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify the fractions:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );