document.write( "Question 1006746: Let B =(
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\n" ); document.write( "a)Find det(B) in terms of k;
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Algebra.Com's Answer #622833 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"B+=%28matrix+%283%2C3%2C1%2C2%2C3%2C2%2Ck-3%2C3%2C3%2C4%2Ck-4%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "I'll do the first part, part (a), to get you started\r
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\n" ); document.write( "\n" ); document.write( "I'm using the method shown below\r
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\n" ); document.write( "\n" ); document.write( "Using that method, we can say\r
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\n" ); document.write( "\n" ); document.write( "Let's compute the sub-determinants (the determinants of the 2x2 submatrices)\r
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\n" ); document.write( "\n" ); document.write( "\"abs%28matrix+%282%2C2%2Ck-3%2C3%2C4%2Ck-4%29%29+=+%28k-3%29%28k-4%29-4%2A3\"\r
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\n" ); document.write( "\n" ); document.write( "\"abs%28matrix+%282%2C2%2Ck-3%2C3%2C4%2Ck-4%29%29+=+k%5E2-7k%2B12-12\"\r
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\n" ); document.write( "\n" ); document.write( "\"abs%28matrix+%282%2C2%2Ck-3%2C3%2C4%2Ck-4%29%29+=+k%5E2-7k\"
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\n" ); document.write( "\"abs%28matrix+%282%2C2%2C2%2C3%2C3%2Ck-4%29%29=2%2A%28k-4%29-3%2A3\"\r
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\n" ); document.write( "\n" ); document.write( "\"abs%28matrix+%282%2C2%2C2%2C3%2C3%2Ck-4%29%29=2k-8-9\"\r
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\n" ); document.write( "\n" ); document.write( "\"abs%28matrix+%282%2C2%2C2%2C3%2C3%2Ck-4%29%29=2k-17\"
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\n" ); document.write( "\"abs%28matrix+%282%2C2%2C2%2Ck-3%2C3%2C4%29%29=2%2A4-3%2A%28k-3%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"abs%28matrix+%282%2C2%2C2%2Ck-3%2C3%2C4%29%29=8-3k%2B9\"\r
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\n" ); document.write( "\n" ); document.write( "\"abs%28matrix+%282%2C2%2C2%2Ck-3%2C3%2C4%29%29=-3k%2B17\"
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\n" ); document.write( "\n" ); document.write( "Now let's return to the determinant of the 3x3 matrix.\r
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\n" ); document.write( "\n" ); document.write( "\"det%28B%29+=+1%2A%28k%5E2-7k%29%2B%28-2%29%2A%282k-17%29%2B3%2A%28-3k%2B17%29\" Make the proper substitutions (see the sub-determinants above)\r
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\n" ); document.write( "\n" ); document.write( "\"det%28B%29+=+k%5E2-7k-4k%2B34-9k%2B51\" Distribute\r
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\n" ); document.write( "\n" ); document.write( "\"det%28B%29+=+k%5E2-20k%2B85\" Combine like terms. This is the final answer for part (a)
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