document.write( "Question 1205181: Consider the following system of linear equations
\n" ); document.write( "𝑥 + 3𝑦 + 2𝑧 - 𝑤 = −1
\n" ); document.write( "−3𝑥 − 7𝑦 + (𝑝 − 6)𝑧 + 2𝑤 = 1
\n" ); document.write( "2𝑥 + 𝑝^2𝑧 + 𝑝𝑤 = 𝑞^2
\n" ); document.write( "where 𝑝 and 𝑞 are real numbers.
\n" ); document.write( "Using Gaussian elimination, determine all possible values of 𝑝 and 𝑞 such that the system has no solution. \n" ); document.write( "

Algebra.Com's Answer #841824 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Write the augmented matrix for the given system of equations.\r\n" );
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document.write( "A augmented matrix has no solution if a row \r\n" );
document.write( "has all 0's except for a non-zero element, say 1,\r\n" );
document.write( "for the rightmost element.  For it would\r\n" );
document.write( "represent the equation 0x+0y+0z+0w=1.\r\n" );
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document.write( "We try to get a row with all 0's except for\r\n" );
document.write( "a non-zero element for a rightmost element.\r\n" );
document.write( "Multiply row 1 by 3 and add to row 2:\r\n" );
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document.write( "Multiply row 1 by -2 and add to row 3:\r\n" );
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document.write( "Multiply row 2 by 3 and add to row 3:\r\n" );
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document.write( "The bottom row will represent an equation with\r\n" );
document.write( "no solution if:\r\n" );
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document.write( "If p=1, the first two equations will be true.\r\n" );
document.write( "The inequality will hold if \r\n" );
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document.write( "Answer: , \r\n" );
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document.write( "Edwin

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