document.write( "Question 443287: I am stuck on a project, and am desperate for help. My teacher denied me any help during class, so I'm kind of packed into a corner.
\n" ); document.write( "1. I have to write an augmented matrix using this system : 2x=5y 3y+x=-11
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Algebra.Com's Answer #305857 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
I am stuck on a project, and am desperate for help. My teacher denied me any help during class, so I'm kind of packed into a corner.
\n" ); document.write( "1. I have to write an augmented matrix using this system : 2x=5y 3y+x=-11
\n" ); document.write( "2.After I find the augmented matrix, I have to find two matrices that multiply to a product of the augmented matrix.
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document.write( "\"system%282x=5y%2C3y%2Bx=-11%29\"\r\n" );
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document.write( "Get the equations in general form:\r\n" );
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document.write( "\"system%282x-5y=0%2C1x%2B3y=-11%29\"\r\n" );
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document.write( "The augmented matrix is just an array of all the numbers\r\n" );
document.write( "in the system without the letters or equal signs:\r\n" );
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document.write( "\"%28matrix%282%2C3%2C%0D%0A%0D%0A+2%2C-5%2C0%2C%0D%0A+1%2C+3%2C-11%29%29\"\r\n" );
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document.write( "That's a 2x3 matrix.\r\n" );
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document.write( "To find two matrices that have a 2x3 matrix as their\r\n" );
document.write( "product, the first could be a 2x2 and the second a 2x3\r\n" );
document.write( "matrix. \r\n" );
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document.write( "Let's make up an arbitrary 2x2 matrix, say\r\n" );
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document.write( "\"%28matrix%282%2C2%2C2%2C3%2C1%2C-4%29%29\"\r\n" );
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document.write( "Then we'll let the 2x3 matrix be:\r\n" );
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document.write( "\"%28matrix%282%2C3%2Cp%2Cq%2Cr%2Cs%2Ct%2Cu%29%29\"\r\n" );
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document.write( "So we have\r\n" );
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document.write( "Equating elements of the two 2x3 matrices:, we have \r\n" );
document.write( "these 3 systems of equations:\r\n" );
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document.write( "\"system%282p%2B3s=2%2Cp-4s=1%29\", \"system%282q%2B3t=-5%2Cq-4t=3%29\", \"system%282r%2B3u=0%2Cr-4u=-11%29\", \r\n" );
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document.write( "We solve those 3 systems and get p=1,s=0, q=-1,t=-1,r=-3,u=2\r\n" );
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document.write( "So one possible answer is\r\n" );
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document.write( "  \r\n" );
document.write( "But you could make up any (non-singular) 2x2 matrix\r\n" );
document.write( "and find a 2x3 matrix so that the product would be\r\n" );
document.write( "equal to the augmented matrix.  There are many possible\r\n" );
document.write( "answers, in fact infinitely many.\r\n" );
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document.write( "Edwin
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