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Utilitzant el mètode de Gauss per a resoldre el sistema<br /><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#p1«/mi»«mo»=«/mo»«mi»#d1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#p21«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mi»#d21«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#p3«/mi»«mo»=«/mo»«mi»#d3«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»</span><br />arribem a la sistema equivalent següent:<br /><span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨¨»«mtable»«mtr»«mtd»«mi»#p1«/mi»«mo»=«/mo»«mi»#d1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#p2«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mi»#d2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«mo»=«/mo»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»</span><br />Això ens indica que el sistema és:<br />
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Choice 1
Answer
un sistema compatible determinat
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Una equació del tipus 0 = 0 no aporta informació addicional i cal eliminar-la. Llavors, una de les incògnites passa a ser una variable i les altres incògnites depenen del seu valor. Per tant, la solució del sistema no és única i el sistema no és compatible determinat. El sistema té infinites solucions (una per cada valor de la variable).
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Choice 2
Answer
un sistema compatible indeterminat
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Feedback
Molt bé. Una equació del tipus 0 = 0 no aporta informació addicional i cal eliminar-la. Llavors, una de les incògnites passa a ser una variable i les altres incògnites depenen del seu valor. Per tant, la solució del sistema no és única sinó que té infinites solucions (per exemple una per cada valor de la variable z)<br /><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»x«/mi»«mo»=«/mo»«mi»#x1«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«mo»=«/mo»«mi»#y1«/mi»«mo»,«/mo»«mi»z«/mi»«mo»=«/mo»«mi»z«/mi»«/math»</span><br /><br /><br />
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Choice 3
Answer
un sistema incompatible
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Feedback
Atenció, si es tractés d'un sistema incompatible hauríem arribat a una expressió impossible, a una igualtat que no sigui mai certa. L'expressió 0 = 0 no és una expressió impossible sinó una expressió que no aporta informació, sempre és certa.
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Choice 4
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Choice 5
Answer
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Choice 6
Answer
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Wednesday, 12 June 2013, 1:03 PM
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