document.write( "Question 1079389: solve the following simultenous equations by inverse and matrix method
\n" ); document.write( "{3a+3b+c=21}
\n" ); document.write( "{5a+10b+2c=52)
\n" ); document.write( "{8a+32b+4c=136}\r
\n" ); document.write( "\n" ); document.write( "Thank you.\r
\n" ); document.write( "\n" ); document.write( "Jane \n" ); document.write( "

Algebra.Com's Answer #693703 by Edwin McCravy(20067) $\"\"$ $\"About$

You can put this solution on YOUR website!
Question 485960
\n" ); document.write( "

\r\n" );
document.write( "We convert the system of equations:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "to the matrix equation:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I will assume that you know how to find the inverse of the \r\n" );
document.write( "coefficient matrix.  If not let me know in the thank-you\r\n" );
document.write( "note form below and I'll get back to you by email. It is\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Now we left multiply both sides of the matrix equation by\r\n" );
document.write( "the inverse of the coefficient matrix:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I will also assume that you know how to multiply\r\n" );
document.write( "matrices.  If you don't, let me know below.\r\n" );
document.write( "Multiplying the matrices on the right and\r\n" );
document.write( "multiplying the first two on the left, we get:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That's the identity matrix on the left, which is what you\r\n" );
document.write( "always get when you multiply a matrix by its inverse.\r\n" );
document.write( "Multiplying the identity matrix by the column matrix of \r\n" );
document.write( "variables on the left we get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So a = 2, b = 3, c = 6.\r\n" );
document.write( "\r\n" );
document.write( "Even though I did the entire problem, working with the\r\n" );
document.write( "entire matrix equation, you can see that you can use a \r\n" );
document.write( "shortcut of just doing the right side only, which is to \r\n" );
document.write( "multiply the inverse of the coefficient matrix by the\r\n" );
document.write( "column matrix of constants.  That's because in every \r\n" );
document.write( "case the left side will be the same as above.  \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );