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Ɣ Caso 1:ല��ƵƚŽǀĂůŽƌĞƐ�ĚŝƐƚŝŶƚŽƐ�
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Ɣ Exemplo: 
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Solução: 
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Autovetores: 
 
 
WŽƌƚĂŶƚŽ͕�
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Ɣ Caso 2:ല��ƵƚŽǀĂůŽƌĞƐ�ĐŽŵƉůĞdžŽƐ͗�
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2° Passo: ലĂĐŚĂŶĚŽ�ŽƐ�ĂƵƚŽǀĞƚŽƌĞƐ͘�
KďƐ͗ ŶŽ ĐĂƐŽ Ƶŵ ĂĐŚĂŵŽƐ ŽƐ ĂƵƚŽǀĞƚŽƌĞƐ ĐŽƌƌĞƐƉŽŶĚĞŶƚĞƐ Ă ലലϭലĞ ലലϮ͕ ലŶŽ ĐĂƐŽ Ϯ͕ ĂƵƚŽǀĂůŽƌĞƐ ĐŽŵƉůĞdžŽƐ͕ ǀĂŵŽƐ� � � � � � � � � � � � � � � � � �
ĂĐŚĂƌ ƐŽŵĞŶƚĞ Ƶŵ ĂƵƚŽǀĞƚŽƌ͕ ƉŽƌ ĐŽŶǀĞƌƐĆŽ ƵƐĂŵŽƐ Ž ĂƵƚŽǀĂůŽƌ ĐŽŵ Ă ƉĂƌƚĞ ŝŵĂŐŝŶĂƌŝĂ ƉŽƐŝƚŝǀĂ͕ ŵĂƐ ĐĂƐŽ� � � � � � � � � � � � � � � �
ƋƵĞƌŝĂ�ĨĂnjĞƌ�ĐŽŵ�Ă�ƉĂƌƚĞ�ŶĞŐĂƚŝǀĂ�ƐƵĂ�ƌĞƐƉŽƐƚĂ�ŶĆŽ�ĞƐƚĄ�ĞƌƌĂĚĂ͘�
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K�^͗�WĂƌĂ�ĐĂůĐƵůĂƌ�Ž�tƌŽŶƐŬŝĂŶŽ�ďĂƐƚĂ�ƉĞŐĂƌ�ĂƉĞŶĂƐ�LJϭ�Ğ�LJϮ͕�ŶĆŽ�Ġ�ŶĞĐĞƐƐĄƌŝŽ�ĚĞƌŝǀĂƌ͘�
Ɣ �ĂƐŽ�ϯ͗��ƵƚŽǀĂůŽƌĞƐ�ƌĞƉĞƚŝĚŽƐ�
YƵĂŶĚŽ ƚĞŵŽƐ ലɉ ƌĞƉĞƚŝĚŽƐ͕ ƚĞƌĞŵŽƐ ĂƵƚŽǀĂůŽƌĞƐ ůŝŶĞĂƌŵĞŶƚĞ ĚĞƉĞŶĚĞŶƚĞƐ͕ ƉĂƌĂ ƐŽůƵĐŝŽŶĂƌ ĞƐƐĞ� � � � � � � � � � �
ĐĂƐŽ ďĂƐƚĂ ĨĂnjĞƌŵŽƐ ĐŽŵŽ ĞƌĂ Ğŵ ��K ĚĞ Ϯǐ ŽƌĚĞŵ͕ ŵƵůƚŝƉůŝĐĂƌ ƉĞůĂ ŵĞŶŽƌ ƉŽƚġŶĐŝĂ ĚĞ ͞ƚ͟ Ğ ĚŝǀŝĚŝƌ ƉĞůŽ� � � � � � � � � � � � � � � � � � �
ĨĂƚŽƌŝĂů�ĐŽƌƌĞƐƉŽŶĚĞŶƚĞ�ĚĞ�ƐƵĂ�ƉŽƐŝĕĆŽ�ƉĂƌĂ�ĚĞŝdžĂƌ�Ž�ƚĞƌŵŽ�ůŝŶĞĂƌŵĞŶƚĞ�ŝŶĚĞƉĞŶĚĞŶƚĞ͘�
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&ŽƌŵĂůŝnjĂĕĆŽ͗�
^Ğ�ŚĄ�ĂƉĞŶĂƐ�Ƶŵ�<�Ă�ലɉͳԞ͖�ƚĞŵŽƐ͗�
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WĞƌĐĞďĂ�ƋƵĞ�ƚŽĚŽƐ�ƐĆŽ�ലɉͳԞ͕�ƌĞƉĂƌĞ�ƚĂŵďĠŵ�ŶĂƐ�ƉŽƚġŶĐŝĂƐ�ĚĞ�ƚ�Ğ�ƐĞƵƐ�ĨĂƚŽƌŝĂŝƐ�ĚĞ�ƐƵĂ�ƉŽƐŝĕĆŽ͘�
�ůŐƵŶƐ ĐĂƐŽƐ͕ ŵĞƐŵŽ ƚĞŶĚŽ ĂƵƚŽǀĂůŽƌĞƐ ŝŐƵĂŝƐ͕ ĞůĞƐ ĂŝŶĚĂ ƉŽĚĞŵ ŐĞƌĂƌ Ϯ ĂƵƚŽǀĞƚŽƌĞƐ >͘/͕͘ ŶĞƐƐĞ� � � � � � � � � � � � � �
ĐĂƐŽ�ŶĆŽ�ŚĄ�ŶĞĐĞƐƐŝĚĂĚĞ�ĚĞ�ŵƵůƚŝƉůŝĐĂƌŵŽƐ�ƉĞůĂ�ŵĞŶŽƌ�ƉŽƚġŶĐŝĂ͘�
Ɣ �džĞŵƉůŽ͗�
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DĂŶŝƉƵůĂŶĚŽ�ŽƐ�ƐŝƐƚĞŵĂƐ͕�ĐŚĞŐĂŵŽƐ�Ă�ƐĞŐƵŝŶƚĞ�ĞdžƉƌĞƐƐĆŽ͗�
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WŽƌƚĂŶƚŽ͕�ƚĞŵŽƐ�Ϯ�ĂƵƚŽǀĞƚŽƌĞƐ͘�
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WŽƌ�Ĩŝŵ͕�ĨĂnjĞŶĚŽ�ƉĂƌĂ�ലɉʹαͷԞ͘�
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�ŚĞŐĂŵŽƐ�Ă�ĞdžƉƌĞƐƐĆŽ͗�ലǦȾαɀαȽ�
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�ŶƚĆŽ�ĐŚĞŐĂŵŽƐ�ă�ƐŽůƵĕĆŽ�ĚŽ�ƐŝƐƚĞŵĂ͗�
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�ŽŶƐŝĚĞƌĂŶĚŽ�ĂŐŽƌĂ�ƋƵĞ�ƚĞŶŚĂŵŽƐ�ĂƵƚŽǀĂůŽƌĞƐ�ŝŐƵĂŝƐ�Ğ�ĂƵƚŽǀĞƚŽƌĞƐ�ŝŐƵĂŝƐ͘�
WĂƌĂ ĞƐƐĞ ƷůƚŝŵŽ ĐĂƐŽ͕ ƚĞŵŽƐ ƋƵĞ ĐŽŶƐŝĚĞƌĂƌ Ă DƵůƚŝƉůŝĐŝĚĂĚĞ ĂůŐĠďƌŝĐĂ ĚŽƐ ĂƵƚŽǀĂůŽƌĞƐ� � � � � � � � � � � �
ĞŶĐŽŶƚƌĂĚŽƐ͘ /ƐƐŽ ƋƵĞƌ ĚŝnjĞƌ ƐĞ ƚŝǀĞƌŵŽƐ Ϯ ĂƵƚŽǀĂůŽƌĞƐ ŝŐƵĂŝƐ͕ ƚĞŵŽƐ ŵƵůƚŝƉůŝĐŝĚĂĚĞ ŝŐƵĂů Ă Ϯ͖ ƐĞ ƚŝǀĞƌŵŽƐ ϯ� � � � � � � � � � � � � � � � �
ĂƵƚŽǀĂůŽƌĞƐ�ŝŐƵĂŝƐ͕�ƚĞŵŽƐ�ŵƵůƚŝƉůŝĐŝĚĂĚĞ�ŝŐƵĂů�Ă�ϯ͘�
^Ğ�Ă�ŵƵůƚŝƉůŝĐŝĚĂĚĞ�ĂůŐĠďƌŝĐĂ�ĨŽƌ�Ϯ͘�
;ല�Ǧɉͳ�ԞͿല�αͲ�
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�ŶƚĆŽ͕�ƚĞƌĞŵŽƐ͗�
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^Ğ Ă ŵƵůƚŝƉůŝĐŝĚĂĚĞ ĂůŐĠďƌŝĐĂ ĨŽƌ ϯ͕ ƚĞŵŽƐ Ă ŵĞƐŵĂ ĞƐƚƌƵƚƵƌĂ ĚŽ Ă ŵƵůƚŝƉůŝĐŝĚĂĚĞ Ϯ͕ ĐŽŵ ƵŵĂ� � � � � � � � � � � � � � � �
ƉĞƋƵĞŶĂ�ŵƵĚĂŶĕĂ͘�
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Ɣ �džĞŵƉůŽ͗�
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KďƚŝǀĞŵŽƐ ĚŽŝƐ ĂƵƚŽǀĂůŽƌĞƐ ŝŐƵĂŝƐ͕ Ă ƉĂƌƚŝƌ ĚŝƐƐŽ͕ ƉŽĚĞŵŽƐ ƚĞƌ ĚŽŝƐ ĂƵƚŽǀĞƚŽƌĞƐ ĚŝƐƚŝŶƚŽƐ ŽƵ ĂƉĞŶĂƐ� � � � � � � � � � � � � �
Ƶŵ ĂƵƚŽǀĞƚŽƌ͕ ĐĂƐŽ ƐĞũĂ ĂƉĞŶĂƐ Ƶŵ͕ ƚĞƌĞŵŽƐ ĚĞ ŵĂŶŝƉƵůĂƌ ĐŽŶĨŽƌŵĞ ŽƐ ĐĂƐŽƐ ĚĂ ŵƵůƚŝƉůŝĐŝĚĂĚĞ ĂůŐĠďƌŝĐĂ� � � � � � � � � � � � � � �
ƉĂƌĂ�ŽďƚĞƌŵŽƐ�ĞdžƉƌĞƐƐƁĞƐ�ůŝŶĞĂƌŵĞŶƚĞ�ŝŶĚĞƉĞŶĚĞŶƚĞƐ͘�
&ĂnjĞŶĚŽ�ƉĂƌĂ�ലɉͳαɉʹαǦ͵�
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KƐ ĂƵƚŽǀĂůŽƌĞƐ ŐĞƌĂƌĂŵ ĂƉĞŶĂƐ Ƶŵ ĂƵƚŽǀĞƚŽƌ͕ ĞŶƚĆŽ ƚĞŵŽƐ ƋƵĞ ĞŶĐŽŶƚƌĂƌ Ƶŵ ŶŽǀŽ ǀĞƚŽƌ ƉĂƌĂ� � � � � � � � � � � � � �
ŐĂƌĂŶƚŝƌ�ƋƵĞ�Ă�ƐŽůƵĕĆŽ�ƐĞũĂ�>͘/͘�
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^ĞŶĚŽ W Ƶŵ ǀĞƚŽƌ >͘/͘ ƉŽĚĞŵŽƐ ĞƐĐŽůŚĞƌ Ƶŵ ǀĂůŽƌ ƉĂƌĂ ലȾ ƋƵĞ Ž ലȽ ǀŝƌĄ ƉŽƌ ĐŽŶƐĞƋƵġŶĐŝĂ Ğ ŶĂ� � � � � � � � � � � � � � � � � � �
ƐŽůƵĕĆŽ�ĨŝŶĂů�ƋƵĂůƋƵĞƌ�ĚĞƐĂũƵƐƚĞ�ƐĞƌĄ�ĐŽŶƐĞƌƚĂĚŽ�ƉĞůĂƐ�ĐŽŶƐƚĂŶƚĞ�ല�ͳǡ�ʹԞ�͘͘͘�ĞƚĐ͘�
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