document.write( "Question 1006746: Let B =(
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document.write( " matrix (3,3,
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document.write( "1,2,3,
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document.write( "2,k-3,3,
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document.write( "3,4,k-4
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document.write( ")
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document.write( "a)Find det(B) in terms of k;
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document.write( "b)For what value(s) of k are the column vectors of B linearly dependent
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document.write( "c)For k = 0, find det(B) and det (-1/2B^tBB^-1) .
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Algebra.Com's Answer #622833 by jim_thompson5910(35256)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "I'll do the first part, part (a), to get you started\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "I'm using the method shown below\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " ![]() \n" ); document.write( "(Image Source: Wikipedia)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Using that method, we can say\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Let's compute the sub-determinants (the determinants of the 2x2 submatrices)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "---------------------------------------------------- \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "---------------------------------------------------- \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "----------------------------------------------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Now let's return to the determinant of the 3x3 matrix.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " |