Pertanyaan

Jika P = [ 1 + x − x ​ x 1 − x ​ ] dan P − 1 adalah invers dari P maka ( P − 1 ) 2 sama dengan matriks ...

Jika  dan  adalah invers dari  maka  sama dengan matriks ...

  1. ...undefined 

  2. ...undefined 

N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

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matriks adalah .

matriks begin mathsize 14px style open parentheses text P end text to the power of negative 1 end exponent close parentheses squared end style adalah begin mathsize 14px style open square brackets table row cell 1 minus 2 x end cell cell negative 2 x end cell row cell 2 x end cell cell 1 plus 2 x end cell end table close square brackets end style.

Pembahasan

Perhatikan perhitungan berikut ini. Invers matriks , yaitu: maka Jadi, matriks adalah .

Perhatikan perhitungan berikut ini.

Invers matriks undefined, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell text P end text to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator text det P end text end fraction text adj P end text end cell row blank equals cell fraction numerator 1 over denominator open parentheses 1 plus x close parentheses open parentheses 1 minus x close parentheses minus open parentheses x close parentheses open parentheses negative x close parentheses end fraction open square brackets table row cell 1 minus x end cell cell negative x end cell row x cell 1 plus x end cell end table close square brackets end cell row blank equals cell fraction numerator 1 over denominator 1 minus x squared plus x squared end fraction open square brackets table row cell 1 minus x end cell cell negative x end cell row x cell 1 plus x end cell end table close square brackets end cell row blank equals cell 1 over 1 open square brackets table row cell 1 minus x end cell cell negative x end cell row x cell 1 plus x end cell end table close square brackets end cell row blank equals cell open square brackets table row cell 1 minus x end cell cell negative x end cell row x cell 1 plus x end cell end table close square brackets end cell end table end style

maka

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses text P end text to the power of negative 1 end exponent close parentheses squared end cell equals cell text P end text to the power of negative 1 end exponent times text P end text to the power of negative 1 end exponent end cell row blank equals cell open square brackets table row cell 1 minus x end cell cell negative x end cell row x cell 1 plus x end cell end table close square brackets open square brackets table row cell 1 minus x end cell cell negative x end cell row x cell 1 plus x end cell end table close square brackets end cell row blank equals cell open square brackets table row cell open parentheses 1 minus x close parentheses open parentheses 1 minus x close parentheses plus open parentheses negative x close parentheses open parentheses x close parentheses end cell cell open parentheses 1 minus x close parentheses open parentheses negative x close parentheses plus open parentheses negative x close parentheses open parentheses 1 plus x close parentheses end cell row cell open parentheses x close parentheses open parentheses 1 minus x close parentheses plus open parentheses 1 plus x close parentheses open parentheses x close parentheses end cell cell open parentheses x close parentheses open parentheses negative x close parentheses plus open parentheses 1 plus x close parentheses open parentheses 1 plus x close parentheses end cell end table close square brackets end cell row blank equals cell open square brackets table row cell 1 minus x minus x plus x squared minus x squared end cell cell negative x plus x squared minus x minus x squared end cell row cell x minus x squared plus x plus x squared end cell cell negative x squared plus 1 plus 2 x plus x squared end cell end table close square brackets end cell row blank equals cell open square brackets table row cell 1 minus 2 x end cell cell negative 2 x end cell row cell 2 x end cell cell 1 plus 2 x end cell end table close square brackets end cell end table end style

Jadi, matriks begin mathsize 14px style open parentheses text P end text to the power of negative 1 end exponent close parentheses squared end style adalah begin mathsize 14px style open square brackets table row cell 1 minus 2 x end cell cell negative 2 x end cell row cell 2 x end cell cell 1 plus 2 x end cell end table close square brackets end style.

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