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Pertanyaan

Diketahui vektor p ​ = ( 3 2 ​ ) , q ​ = ( − 3 − 1 ​ ) dan r → = ( 0 6 ​ ) , tentukan vektor x sehingga persamaan berikut bernilai benar p → ​ + q → ​ + x → = r → .

Diketahui vektor  dan , tentukan vektor  sehingga persamaan berikut bernilai benar .  

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F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

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persamaan berikut bernilai benar saat vektor .

persamaan berikut bernilai benar size 14px p with size 14px rightwards arrow on top size 14px plus size 14px q with size 14px rightwards arrow on top size 14px plus size 14px x with size 14px rightwards arrow on top size 14px equals size 14px r with size 14px rightwards arrow on top saat vektor begin mathsize 14px style x with rightwards arrow on top equals open parentheses table row 0 row 5 end table close parentheses end style.

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Pembahasan

Vektor sehingga bernilai benar, dapat dicari dengan melakukan substitusi vektor-vektor dan pada persamaan. Misal: , maka Jadi, persamaan berikut bernilai benar saat vektor .

Vektor begin mathsize 14px style x with rightwards arrow on top end style sehingga size 14px p with size 14px rightwards arrow on top size 14px plus size 14px q with size 14px rightwards arrow on top size 14px plus size 14px x with size 14px rightwards arrow on top size 14px equals size 14px r with size 14px rightwards arrow on top bernilai benar, dapat dicari dengan melakukan substitusi vektor-vektor  begin mathsize 14px style stack text p end text with rightwards arrow on top equals open parentheses table row 3 row 2 end table close parentheses comma space stack text q end text with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row cell negative 1 end cell end table close parentheses end style dan undefined pada persamaan.

Misal: undefined, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row 3 row 2 end table close parentheses plus open parentheses table row cell negative 3 end cell row cell negative 1 end cell end table close parentheses plus open parentheses table row cell x subscript 1 end cell row cell x subscript 2 end cell end table close parentheses end cell equals cell open parentheses table row 0 row 6 end table close parentheses end cell row cell open parentheses table row 0 row 1 end table close parentheses plus open parentheses table row cell x subscript 1 end cell row cell x subscript 2 end cell end table close parentheses end cell equals cell open parentheses table row 0 row 6 end table close parentheses end cell row cell open parentheses table row cell x subscript 1 end cell row cell x subscript 2 end cell end table close parentheses end cell equals cell open parentheses table row 0 row 6 end table close parentheses minus open parentheses table row 0 row 1 end table close parentheses end cell row cell open parentheses table row cell x subscript 1 end cell row cell x subscript 2 end cell end table close parentheses end cell equals cell open parentheses table row 0 row 5 end table close parentheses end cell row blank rightwards arrow cell x subscript 1 equals 0 logical and x subscript 2 equals 5 end cell end table end style

Jadi, persamaan berikut bernilai benar size 14px p with size 14px rightwards arrow on top size 14px plus size 14px q with size 14px rightwards arrow on top size 14px plus size 14px x with size 14px rightwards arrow on top size 14px equals size 14px r with size 14px rightwards arrow on top saat vektor begin mathsize 14px style x with rightwards arrow on top equals open parentheses table row 0 row 5 end table close parentheses end style.

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