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March 21st, 2015, 06:07 PM   #1
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From: dy/dx = dy/du X du/dx 9. CHAIN

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11.3, homogeneous systems, linear al

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Attached Images Capture12.JPG (30.5 KB, 3 views) March 22nd, 2015, 05:17 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 If your question is "How can I look at this and instantly know the answer without doing any work?", I can't help you because I can't do that myself! Do you understand that this matrix equation is equivalent to the three simultaneous equations $\displaystyle x_1 + 3x_2 - 5x_3 + x_4 + 3x_5 + 2x_6 = 0$ $\displaystyle x_3 + 5x_4 + 2x_6 = 0$ $\displaystyle x_5 - x_6 = 0$? Surely you can see that the last equation is the same as $\displaystyle x_5 = x_6$. We can also solve the second equation for $\displaystyle x_3$: $\displaystyle x_3 = -x_4- 2x_6$ Replacing $\displaystyle x_3$ and $\displaystyle x_5$ in the first equation by those, $\displaystyle x_1 + 3x_2- 5(-x_4 - 2x_6) + x_4 + 3(x_6) + 2x_6 = x_1 + 3x_2 + 6x_4 + 15x_6 = 0$ So $\displaystyle x_1= -3x_2 - 6x_4 - 15x_6 = 0$ and now all can be written in terms of $\displaystyle x_2$, $\displaystyle x_4$, and $\displaystyle x_6$. Last edited by skipjack; March 22nd, 2015 at 06:43 PM. Tags 113, homogeneous, linear, systems Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post philip Calculus 5 February 22nd, 2013 09:40 AM tools Linear Algebra 1 September 21st, 2012 12:38 PM oasi Calculus 2 March 14th, 2012 01:50 PM mbradar2 Calculus 7 October 23rd, 2010 08:56 PM remeday86 Linear Algebra 1 June 27th, 2010 11:58 AM

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