document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188320>Question 188320</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780132402866/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> use properties of determinants to find the value of each determinant if it is know that <BR>\n" );
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document.write( "|1 2 3| =4\r<BR>\n" );
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document.write( "|2 4 6| </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141161 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=141161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember, you can multiply a scalar value \"k\" by any row of a determinant like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2Aabs%28matrix%283%2C3%2Ca%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29=abs%28matrix%283%2C3%2Ck%2Aa%2Ck%2Ab%2Ck%2Ac%2Cd%2Ce%2Cf%2Cg%2Ch%2Ci%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Note: you can pick any row. In this example, I'm using the first row.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C1%2C2%2C3%29%29=4 ALIGN=MIDDLE  ALT=\"abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C1%2C2%2C3%29%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "Since the bottom row of the resulting determinant is 2, 4, and 6 this means that this row is 2 times the bottom row of the given determinant.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aabs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C1%2C2%2C3%29%29=2%2A4 ALIGN=MIDDLE  ALT=\"2%2Aabs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C1%2C2%2C3%29%29=2%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C2%2A1%2C2%2A2%2C2%2A3%29%29=2%2A4 ALIGN=MIDDLE  ALT=\"abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C2%2A1%2C2%2A2%2C2%2A3%29%29=2%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the scalar 2 by the entire bottom row of the determinant\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C2%2C4%2C6%29%29=8 ALIGN=MIDDLE  ALT=\"abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C2%2C4%2C6%29%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C2%2C4%2C6%29%29=8 ALIGN=MIDDLE  ALT=\"abs%28matrix%283%2C3%2Cx%2Cy%2Cz%2Cu%2Cv%2Cw%2C2%2C4%2C6%29%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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