document.write( "Question 1148590: consider the matrix p (t+2 3t t+1)
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\n" ); document.write( "for what value or values of t does matrix p has zero as its determinant \n" ); document.write( "
Algebra.Com's Answer #769932 by ikleyn(52810)\"\" \"About 
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document.write( "The matrix is\r\n" );
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document.write( "    P = \"%28matrix%283%2C3%2C+t%2B2%2C+3t%2C+t%2B1%2C++0%2C+t-1%2C+0%2C++2t%2B4%2C+t%2C+3t%2B1%29%29\"\r\n" );
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document.write( "If you write all 6 the determinant's terms, 4 of them (out-the-diagonals-terms) will contain 0 (zero) as a factor, \r\n" );
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document.write( "and, therefore, will be equal to zero.\r\n" );
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document.write( "The only two diagonal terms will contribute to the determinant\r\n" );
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document.write( "    det(P) = (t+2)*(t-1)*(3t+1) - (2t+4)*(t-1)*(t+1) = (t-1)*((t+2)*(3t+1) - (2t+4)*(t+1)) = \r\n" );
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document.write( "           = (t-1)*(t+2)*((3t+1) - 2*(t+1)) = (t-1)*(t+2)*(t-1) = (t+2)*(t-1)^2.\r\n" );
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document.write( "The zeroes of the determinant are the values t= -2 (of multiplicity 1) and t= 1 (of multiplicity 2).\r\n" );
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\n" ); document.write( "\n" ); document.write( "On introductory lessons on determinants of 3x3-matrices see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Determinant of a 3x3 matrix \r
\n" ); document.write( "\n" ); document.write( "    - Co-factoring the determinant of a 3x3 matrix \r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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