Jika vektor dan . Vektor

Pertanyaan

Jika vektor $straight a with rightwards arrow on top equals open parentheses table row 1 row 2 row 3 end table close parentheses comma space straight b with rightwards arrow on top equals open parentheses table row 5 row 4 row cell negative 1 end cell end table close parentheses$ dan $straight c with rightwards arrow on top equals open parentheses table row 4 row cell negative 1 end cell row 1 end table close parentheses$ . Vektor $straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top minus 3 straight c with rightwards arrow on top equals space...$

Pembahasan Soal:

Diketahui $straight a with rightwards arrow on top equals open parentheses table row 1 row 2 row 3 end table close parentheses comma space straight b with rightwards arrow on top equals open parentheses table row 5 row 4 row cell negative 1 end cell end table close parentheses$ dan $straight c with rightwards arrow on top equals open parentheses table row 4 row cell negative 1 end cell row 1 end table close parentheses$ , maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top minus 3 straight c with rightwards arrow on top end cell equals cell open parentheses table row 1 row 2 row 3 end table close parentheses plus 2 open parentheses table row 5 row 4 row cell negative 1 end cell end table close parentheses minus 3 open parentheses table row 4 row cell negative 1 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row 1 row 2 row 3 end table close parentheses plus open parentheses table row 10 row 8 row cell negative 2 end cell end table close parentheses minus open parentheses table row 12 row cell negative 3 end cell row 3 end table close parentheses end cell row blank equals cell open parentheses table row cell 1 plus 10 minus 12 end cell row cell 2 plus 8 minus open parentheses negative 3 close parentheses end cell row cell 3 plus open parentheses negative 2 close parentheses minus 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row 13 row cell negative 2 end cell end table close parentheses end cell end table$

Jadi, $straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top minus 3 straight c with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 13 row cell negative 2 end cell end table close parentheses$ .

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

L. Rante

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 04 Juni 2021

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Diketahui vektor-vektor , , dan . Vektor . Dalam bentuk vektor basis adalah ....

Pembahasan Soal:

Diketahui vektor-vektor $p with bar on top equals open parentheses table row 4 row cell negative 2 end cell end table close parentheses$ , $q with bar on top equals open parentheses table row 9 row cell negative 6 end cell end table close parentheses$ , dan $r with bar on top equals open parentheses table row 4 row 6 end table close parentheses$ . Vektor $s with bar on top equals 1 half p with bar on top minus 1 third q with bar on top plus 1 fourth r with bar on top$ dapat dinyatakan sebagai berikut

$table attributes columnalign right center left columnspacing 0px end attributes row cell s with bar on top end cell equals cell 1 half open parentheses table row 4 row cell negative 2 end cell end table close parentheses minus 1 third open parentheses table row 9 row cell negative 6 end cell end table close parentheses plus 1 fourth open parentheses table row 4 row 6 end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative 1 end cell end table close parentheses minus open parentheses table row 3 row cell negative 2 end cell end table close parentheses plus open parentheses table row 1 row cell 6 over 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 minus 3 plus 1 end cell row cell negative 1 plus 2 plus 6 over 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell 4 over 4 plus 6 over 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell 10 over 4 end cell end table close parentheses end cell row blank equals cell negative 10 over 4 j end cell end table$

Jadi, $s with bar on top equals negative 10 over 4 j$ .

Roboguru

Diketahui vektor-vektor , , dan . Maka hitunglah vektor .

Pembahasan Soal:

Jika terdapat vektor $a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses$ dan skalar $k$ , maka perkalian vektor dengan skalar adalah:

$table attributes columnalign right center left columnspacing 0px end attributes row cell k a with rightwards arrow on top end cell equals cell k open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell k a subscript 1 end cell row cell k a subscript 2 end cell end table close parentheses end cell end table$

Diketahui $a with rightwards arrow on top equals open parentheses table row 3 row 5 end table close parentheses$ , $b with rightwards arrow on top equals open parentheses table row 2 row 1 end table close parentheses$ , dan $c with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 8 end table close parentheses$ . Maka vektor $2 italic a with rightwards arrow on top minus sign italic b with rightwards arrow on top plus 1 half italic c with rightwards arrow on top$ adalah:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 a with rightwards arrow on top minus b with rightwards arrow on top plus 1 half c with rightwards arrow on top end cell row blank equals cell 2 open parentheses table row 3 row 5 end table close parentheses minus open parentheses table row 2 row 1 end table close parentheses plus 1 half open parentheses table row cell negative 4 end cell row 8 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 times 3 end cell row cell 2 times 5 end cell end table close parentheses minus open parentheses table row 2 row 1 end table close parentheses plus open parentheses table row cell fraction numerator negative 4 over denominator 2 end fraction end cell row cell 8 over 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 6 row 10 end table close parentheses minus open parentheses table row 2 row 1 end table close parentheses plus open parentheses table row cell negative 2 end cell row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 6 minus 2 plus open parentheses negative 2 close parentheses end cell row cell 10 minus 1 plus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row 13 end table close parentheses end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell c with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 2 row 13 end table close parentheses end cell end table$ .

Roboguru

Diketahui vektor Tentukan hasil dari .

Pembahasan Soal:

Operasi pada vektor

Diketahui vektor

$a with bar on top equals 3 i with hat on top plus 2 j with hat on top minus k with hat on top b with bar on top equals 3 i with hat on top plus 5 j with hat on top plus 4 k with hat on top a with bar on top equals negative 5 i with hat on top plus 2 j with hat on top minus 3 k with hat on top$

Akan ditentukan hasil dari $negative 3 c with bar on top plus 3 a with bar on top minus 2 b with bar on top$

$table attributes columnalign right center left columnspacing 0px end attributes row cell negative 3 c with bar on top plus 3 a with bar on top minus 2 b with bar on top end cell equals cell negative 3 open parentheses negative 5 i with hat on top plus 2 j with hat on top minus 3 k with hat on top close parentheses plus 3 open parentheses 3 i with hat on top plus 2 j with hat on top minus k with hat on top close parentheses minus 2 open parentheses 3 i with hat on top plus 5 j with hat on top plus 4 k with hat on top close parentheses end cell row blank equals cell 15 i with hat on top minus 6 j with hat on top plus 9 k with hat on top plus 9 i with hat on top plus 6 j with hat on top minus 3 k with hat on top minus 6 i with hat on top minus 10 j with hat on top minus 8 k with hat on top end cell row blank equals cell open parentheses 15 plus 9 minus 6 close parentheses i with hat on top plus open parentheses negative 6 plus 6 minus 10 close parentheses j with hat on top plus open parentheses 9 minus 3 minus 8 close parentheses k with hat on top end cell row blank equals cell 18 i with hat on top plus negative 10 minus 2 k with hat on top end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row cell negative 3 c with bar on top plus 3 a with bar on top minus 2 b with bar on top end cell equals cell 18 i with hat on top plus negative 10 minus 2 k with hat on top end cell end table$ .

Roboguru

Diketahui vektor-vektor , , dan . Hasil dari adalah... .

Pembahasan Soal:

Diketahui vektor-vektor $p with rightwards arrow on top equals 10 i with rightwards arrow on top minus 3 j with rightwards arrow on top$ , $q with rightwards arrow on top equals 3 i with rightwards arrow on top plus 2 j with rightwards arrow on top minus k with rightwards arrow on top$ , dan $r with rightwards arrow on top equals 4 j with rightwards arrow on top plus 7 k with rightwards arrow on top$ . Vektor tersebut jika diubah menjadi vektor kolom menjadi $p with rightwards arrow on top equals open parentheses table row 10 row cell negative 3 end cell row 0 end table close parentheses$ , $q with rightwards arrow on top equals open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses$ , dan $r with rightwards arrow on top equals open parentheses table row 0 row 4 row 7 end table close parentheses$ . Hasil dari $3 p with rightwards arrow on top minus q with rightwards arrow on top plus 2 r with rightwards arrow on top$ sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell 3 p with rightwards arrow on top minus q with rightwards arrow on top plus 2 r with rightwards arrow on top end cell equals cell 3 open parentheses table row 10 row cell negative 3 end cell row 0 end table close parentheses minus open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses plus 2 open parentheses table row 0 row 4 row 7 end table close parentheses end cell row blank equals cell open parentheses table row 30 row cell negative 9 end cell row 0 end table close parentheses minus open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses plus open parentheses table row 0 row 8 row 14 end table close parentheses end cell row blank equals cell open parentheses table row cell 30 minus 3 plus 0 end cell row cell negative 9 minus 2 plus 8 end cell row cell 0 minus open parentheses negative 1 close parentheses plus 14 end cell end table close parentheses end cell row blank equals cell open parentheses table row 27 row cell negative 3 end cell row 15 end table close parentheses end cell row blank equals cell 27 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 15 k with rightwards arrow on top end cell end table$

Hasil dari $3 p with rightwards arrow on top minus q with rightwards arrow on top plus 2 r with rightwards arrow on top$ yaitu $27 i with rightwards arrow on top minus 3 j with rightwards arrow on top plus 15 k with rightwards arrow on top$ .

Jadi, jawaban yang benar adalah C.

Roboguru

Tentukan hasil operasi vektor berikut. a. b. c.

Pembahasan Soal:

Ingat : $begin mathsize 14px style open parentheses table row a row b end table close parentheses plus-or-minus open parentheses table row c row d end table close parentheses equals open parentheses table row cell a plus-or-minus c end cell row cell b plus-or-minus d end cell end table close parentheses end style$

Jadi,

a. $begin mathsize 14px style open parentheses table row 4 row 3 end table close parentheses plus open parentheses table row cell negative 2 end cell row 5 end table close parentheses equals open parentheses table row 2 row 8 end table close parentheses end style$

b. $begin mathsize 14px style open parentheses table row 7 row 4 end table close parentheses minus open parentheses table row 3 row cell negative 1 end cell end table close parentheses equals open parentheses table row 4 row 5 end table close parentheses end style$

c. $begin mathsize 14px style open parentheses table row cell negative 5 end cell row 6 end table close parentheses plus open parentheses table row 8 row 4 end table close parentheses plus open parentheses table row cell negative 3 end cell row cell negative 2 end cell end table close parentheses equals open parentheses table row 0 row 8 end table close parentheses end style$

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