Roboguru

Diketahui  dan  dan matriks , invers dari matriks  adalah ...

Pertanyaan

Diketahui begin mathsize 14px style straight A equals open parentheses table row 3 cell negative 1 end cell row cell negative 1 end cell 1 end table close parentheses end style dan begin mathsize 14px style straight B equals open parentheses table row 2 1 row 1 5 end table close parentheses end style dan matriks begin mathsize 14px style straight C equals straight B minus straight A end style, invers dari matriks begin mathsize 14px style straight C end style adalah ... 

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight C equals cell straight B minus straight A end cell row blank equals cell open parentheses table row 2 1 row 1 5 end table close parentheses minus open parentheses table row 3 cell negative 1 end cell row cell negative 1 end cell 1 end table close parentheses end cell row straight C equals cell open parentheses table row cell negative 1 end cell 2 row 2 4 end table close parentheses end cell end table end style 

Determinan matriks C adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight C close vertical bar end cell equals cell open parentheses negative 1 close parentheses times 4 minus 2 times 2 end cell row blank equals cell negative 4 minus 4 end cell row blank equals cell negative 8 end cell end table end style 

Invers matriks C adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight C to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator open vertical bar straight C close vertical bar end fraction open parentheses table row 4 cell negative 2 end cell row cell negative 2 end cell cell negative 1 end cell end table close parentheses space end cell row blank equals cell fraction numerator 1 over denominator negative 8 end fraction open parentheses table row 4 cell negative 2 end cell row cell negative 2 end cell cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 half end cell cell 1 fourth end cell row cell 1 fourth end cell cell 1 over 8 end cell end table close parentheses end cell end table end style  

Jadi invers matriks C adalah begin mathsize 14px style straight C to the power of negative 1 end exponent equals open parentheses table row cell negative 1 half end cell cell 1 fourth end cell row cell 1 fourth end cell cell 1 over 8 end cell end table close parentheses end style.  

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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