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Diketahui A = ( 1 − 1 ​ 2 − 1 ​ ) , B = ( 1 0 ​ 1 − 1 ​ ) ,dan C = ( 0 − 1 ​ 1 0 ​ ) . Tentukan: a. A 2 + B 3 − C 3

Diketahui , , dan . Tentukan:

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I. Ridha

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

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Pembahasan

Dengan menyubtitusikan ke , diperoleh: Dengan menyubtitusikan ke , diperoleh: Dengan menyubtitusikan ke , diperoleh: Dengan demikian, diperoleh:

Dengan menyubtitusikan A equals open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses ke A squared, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell A squared end cell equals cell open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses squared end cell row blank equals cell open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 open parentheses 1 close parentheses plus 2 open parentheses negative 1 close parentheses end cell cell 1 open parentheses 2 close parentheses plus 2 open parentheses negative 1 close parentheses end cell row cell negative 1 open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses end cell cell negative 1 open parentheses 2 close parentheses plus open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 plus open parentheses negative 2 close parentheses end cell cell 2 plus open parentheses negative 2 close parentheses end cell row cell open parentheses negative 1 close parentheses plus 1 end cell cell open parentheses negative 2 close parentheses plus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses end cell end table

Dengan menyubtitusikan B equals open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses ke B squared, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell B cubed end cell equals cell open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses cubed end cell row blank equals cell open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 open parentheses 1 close parentheses plus 1 open parentheses 0 close parentheses end cell cell 1 open parentheses 1 close parentheses plus 1 open parentheses negative 1 close parentheses end cell row cell 0 open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses open parentheses 0 close parentheses end cell cell 0 open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses end cell end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses subscript table attributes columnalign left end attributes row cell space space space space space karena space open parentheses table row 1 0 row 0 1 end table close parentheses space adalah space matriks space identitas end cell row cell space space space space space text maka end text space A I equals A end cell end table end subscript end cell row blank equals cell open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses end cell end table

Dengan menyubtitusikan C equals open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses ke C squared, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell C cubed end cell equals cell open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses cubed end cell row blank equals cell open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row cell 0 open parentheses 0 close parentheses plus 1 open parentheses negative 1 close parentheses end cell cell 0 open parentheses 1 close parentheses plus 1 open parentheses 0 close parentheses end cell row cell open parentheses negative 1 close parentheses open parentheses 0 close parentheses plus 0 open parentheses negative 1 close parentheses end cell cell open parentheses negative 1 close parentheses open parentheses 1 close parentheses plus 0 open parentheses 0 close parentheses end cell end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript text ingat: end text k open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k a end cell cell k b end cell row cell k c end cell cell k d end cell end table close parentheses end subscript end cell row blank equals cell negative 1 open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript table attributes columnalign left end attributes row cell text karena end text open parentheses table row 1 0 row 0 1 end table close parentheses space adalah space matriks space identitas comma end cell row cell space space space space space maka space A I equals A end cell end table text , end text end subscript end cell row blank equals cell negative 1 open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses end cell end table

Dengan demikian, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell A squared plus B cubed minus C cubed end cell equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses plus open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses minus open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 plus 1 minus 0 end cell cell 0 plus 1 minus open parentheses negative 1 close parentheses end cell row cell 0 plus 0 minus 1 end cell cell negative 1 plus open parentheses negative 1 close parentheses minus 0 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 2 row cell negative 1 end cell cell negative 2 end cell end table close parentheses end cell end tablespace 

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