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Pertanyaan

Gambar 3.33 Bentuk-bentuk vektor

a. Nyatakan setiap vektor pada Gambar 3.33 dalam: 

1) vektor kolom, 

2) pasangan terurut, dan 

3) vektor basis.

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

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masing-masing vektor dapat dinyatakan sebagai berikut:

Pembahasan

Ingat bentuk dari:

  • Vektor kolom open parentheses table row x row y end table close parentheses.
  • Pasangan terurut open parentheses x comma space y close parentheses.
  • Vektor basis x i with hat on top plus y j with hat on top.

Berdasarkan bentuk-bentuk di atas, maka vektor tersebut dapat dinyatakan dalam vektor kolom, pasangan terurut, dan vektor basis.

Dengan demikian, masing-masing vektor dapat dinyatakan sebagai berikut:

  • Vektor stack text a end text with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row cell negative 2 end cell end table close parenthesesstack text a end text with rightwards arrow on top equals open parentheses negative 1 comma space minus 2 close parentheses, dan stack text a end text with rightwards arrow on top equals negative i with hat on top minus 2 j with hat on top.
  • Vektor stack text b end text with rightwards arrow on top equals open parentheses table row 3 row 2 end table close parenthesesstack text b end text with rightwards arrow on top equals open parentheses 3 comma space 2 close parentheses, dan stack text b end text with rightwards arrow on top equals 3 i with hat on top plus 2 j with hat on top.
  • Vektor stack text d end text with rightwards arrow on top equals open parentheses table row 1 row 2 end table close parenthesesstack text d end text with rightwards arrow on top equals open parentheses 1 comma space 2 close parentheses, dan stack text d end text with rightwards arrow on top equals i with hat on top plus 2 j with hat on top.
  • Vektor stack text e end text with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row cell negative 3 end cell end table close parenthesesstack text e end text with rightwards arrow on top equals open parentheses negative 2 comma space minus 3 close parentheses, dan stack text e end text with rightwards arrow on top equals negative 2 i with hat on top minus 3 j with hat on top.
  • Vektor stack text f end text with rightwards arrow on top equals open parentheses table row 3 row 1 end table close parenthesesstack text f end text with rightwards arrow on top equals open parentheses 3 comma space 1 close parentheses, dan stack text f end text with rightwards arrow on top equals 3 i with hat on top plus j with hat on top.
  • Vektor stack text r end text with rightwards arrow on top equals open parentheses table row 1 row 3 end table close parenthesesstack text r end text with rightwards arrow on top equals open parentheses 1 comma space 3 close parentheses, dan stack text r end text with rightwards arrow on top equals i with hat on top plus 3 j with hat on top.
  • Vektor stack text s end text with rightwards arrow on top equals open parentheses table row 3 row 2 end table close parenthesesstack text s end text with rightwards arrow on top equals open parentheses 3 comma space 2 close parentheses, dan stack text s end text with rightwards arrow on top equals 3 i with hat on top plus 2 j with hat on top.
  • Vektor stack text t end text with rightwards arrow on top equals open parentheses table row 3 row 1 end table close parenthesesstack text t end text with rightwards arrow on top equals open parentheses 3 comma space 1 close parentheses, dan stack text t end text with rightwards arrow on top equals 3 i with hat on top plus j with hat on top.
  • Vektor stack text u end text with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row cell negative 3 end cell end table close parenthesesstack text u end text with rightwards arrow on top equals open parentheses negative 1 comma space minus 3 close parentheses, dan stack text u end text with rightwards arrow on top equals negative i with hat on top minus 3 j with hat on top.

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