C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes3-2

# C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes3-2 - AB...

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SECTION 3.2 PROPERTIES OF DETERMINANTS Adding a multiple of one row to another row does not change the determinant. Multiplying a row by a constant also multiplies the determinant by that constant. Switching two rows multiplies the determinant by - 1. A square matrix A is invertible if and only if det A 6 = 0, so we have yet another part of the Invertible Matrix Theorem. det A = det A T , so we can do column operations to ﬁnd det A if we want. For square matrices det

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Unformatted text preview: AB = (det A )(det B ). EXAMPLES. Compute ± ± ± ± ± ± ± ± ± 7 3 5 2 4 3-1 5 1-3 2 6-18-9-14 1 ± ± ± ± ± ± ± ± ± Are the vectors 4 6-7 , -7 2 , -3-5 6 linearly independent? Let A and P be square matrices of the same size, with P invertible. Show that 1. det( P-1 ) = 1 / det P , and 2. det( PAP-1 ) = det A. HOMEWORK. SECTION 3.2...
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C__DOCUME~1_MAXWID~1_LOCALS~1_Temp_plugtmp-27_notes3-2 - AB...

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