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Diketahui  jika  dan . Tuliksan  dalam bentuk kom...

Diketahui begin mathsize 14px style stack text AB end text with rightwards harpoon with barb upwards on top end style jika begin mathsize 14px style text A end text open parentheses x subscript 1 comma space y subscript 1 close parentheses end style dan begin mathsize 14px style text B end text open parentheses x subscript 2 comma space y subscript 2 close parentheses end style.

Tuliksan begin mathsize 14px style stack text AB end text with rightwards harpoon with barb upwards on top end style dalam bentuk kombinasi linear!

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Jawaban:

Perhatikan penjelasan berikut ini.

Diketahui begin mathsize 14px style stack text AB end text with rightwards harpoon with barb upwards on top end style jika begin mathsize 14px style text A end text open parentheses x subscript 1 comma space y subscript 1 close parentheses end style dan begin mathsize 14px style text B end text open parentheses x subscript 2 comma space y subscript 2 close parentheses end style. Maka bentuk kombinasi linearnya:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards harpoon with barb upwards on top end cell equals cell stack O B with rightwards harpoon with barb upwards on top minus stack O A with rightwards harpoon with barb upwards on top end cell row blank equals cell open parentheses x subscript 2 comma space y subscript 2 close parentheses minus open parentheses x subscript 1 comma space y subscript 1 close parentheses end cell row blank equals cell open parentheses x subscript 2 minus x subscript 1 comma space y subscript 2 minus y subscript 1 close parentheses end cell row blank equals cell open parentheses x subscript 2 minus x subscript 1 close parentheses k subscript 1 plus open parentheses y subscript 2 minus y subscript 1 close parentheses k subscript 2 end cell end table end style

Dengan begin mathsize 14px style k subscript 1 end style dan begin mathsize 14px style k subscript 2 end style merupakan skalar.

Jadi, kombinasi linear vektor begin mathsize 14px style stack text AB end text with rightwards harpoon with barb upwards on top end style adalah begin mathsize 14px style open parentheses x subscript 2 minus x subscript 1 close parentheses k subscript 1 plus open parentheses y subscript 2 minus y subscript 1 close parentheses k subscript 2 end style.

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