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Diketahui K=(49​12−7​),L=(−30​2−4​), dan M=(04​31​). Tentukan hasil dari matriks berikut (K−L)MT

Pertanyaan

Diketahui K equals open parentheses table row 4 12 row 9 cell negative 7 end cell end table close parentheses comma L equals open parentheses table row cell negative 3 end cell 2 row 0 cell negative 4 end cell end table close parentheses comma spacedan M equals open parentheses table row 0 3 row 4 1 end table close parentheses. Tentukan hasil dari matriks berikut

left parenthesis K minus L right parenthesis M to the power of T 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

diperoleh hasil dari left parenthesis K minus L right parenthesis M to the power of T adalah open parentheses table row 30 38 row cell negative 9 end cell 33 end table close parentheses.

Pembahasan

Diketahui matriks K equals open parentheses table row 4 12 row 9 cell negative 7 end cell end table close parentheses comma L equals open parentheses table row cell negative 3 end cell 2 row 0 cell negative 4 end cell end table close parentheses comma spacedan M equals open parentheses table row 0 3 row 4 1 end table close parentheses

Ingat kembali mengenai operasi perhitungan dalam matriks

Pengurangan Matriks

A minus B equals open parentheses table row cell a subscript 1 end cell cell a subscript 2 end cell row cell a subscript 3 end cell cell a subscript 4 end cell end table close parentheses minus open parentheses table row cell b subscript 1 end cell cell b subscript 2 end cell row cell b subscript 3 end cell cell b subscript 4 end cell end table close parentheses equals open parentheses table row cell a subscript 1 minus b subscript 1 end cell cell a subscript 2 minus b subscript 2 end cell row cell a subscript 3 minus b subscript 3 end cell cell a subscript 4 minus b subscript 4 end cell end table close parentheses 

Perkalian Matriks

A cross times B equals open parentheses table row cell a subscript 1 end cell cell a subscript 2 end cell row cell a subscript 3 end cell cell a subscript 4 end cell end table close parentheses cross times open parentheses table row cell b subscript 1 end cell cell b subscript 2 end cell row cell b subscript 3 end cell cell b subscript 4 end cell end table close parentheses equals open parentheses table row cell a subscript 1 b subscript 1 plus a subscript 2 b subscript 3 end cell cell a subscript 1 b subscript 2 minus a subscript 2 b subscript 4 end cell row cell a subscript 3 b subscript 1 minus a subscript 4 b subscript 3 end cell cell a subscript 3 b subscript 2 minus a subscript 4 b subscript 4 end cell end table close parentheses 

Transpose Matriks

A equals open parentheses table row cell a subscript 1 end cell cell a subscript 2 end cell row cell a subscript 3 end cell cell a subscript 4 end cell end table close parentheses rightwards double arrow A to the power of T equals open parentheses table row cell a subscript 1 end cell cell a subscript 3 end cell row cell a subscript 2 end cell cell a subscript 4 end cell end table close parentheses 

Diperoleh perhitungan sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell K minus L end cell equals cell open parentheses table row 4 12 row 9 cell negative 7 end cell end table close parentheses minus open parentheses table row cell negative 3 end cell 2 row 0 cell negative 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 4 minus left parenthesis negative 3 right parenthesis end cell cell 12 minus 2 end cell row cell 9 minus 0 end cell cell negative 7 minus left parenthesis negative 4 right parenthesis end cell end table close parentheses end cell row blank equals cell open parentheses table row 7 10 row 9 cell negative 3 end cell end table close parentheses space end cell end table 

M equals open parentheses table row 0 3 row 4 1 end table close parentheses rightwards double arrow M to the power of T equals open parentheses table row 0 4 row 3 1 end table close parentheses 

Oleh karena itu, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis K minus L right parenthesis M to the power of T end cell equals cell open parentheses table row 7 10 row 9 cell negative 3 end cell end table close parentheses open parentheses table row 0 4 row 3 1 end table close parentheses end cell row blank equals cell open parentheses table row cell left parenthesis 7 cross times 0 right parenthesis plus left parenthesis 10 cross times 3 right parenthesis end cell cell left parenthesis 7 cross times 4 right parenthesis plus left parenthesis 10 cross times 1 right parenthesis end cell row cell left parenthesis 9 cross times 0 right parenthesis plus left parenthesis negative 3 cross times 3 right parenthesis end cell cell left parenthesis 9 cross times 4 right parenthesis plus left parenthesis negative 3 cross times 1 right parenthesis end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 0 plus 30 end cell cell 28 plus 10 end cell row cell 0 minus 9 end cell cell 36 minus 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 30 38 row cell negative 9 end cell 33 end table close parentheses end cell end table

Dengan demikian, diperoleh hasil dari left parenthesis K minus L right parenthesis M to the power of T adalah open parentheses table row 30 38 row cell negative 9 end cell 33 end table close parentheses.

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