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Diketahui a = 3 i − 2 j ​ , b = − i + 4 j ​ d an r = 7 i − 8 j ​ Jika r = k a + m b maka nilai k + m = …

Diketahui  Jika  maka nilai = …  

  1. -1

  2. 0

  3. 1

  4. 2

  5. 3

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Pembahasan

Sehingga didapatkan dua buah persamaan 3 k - m = 7 - 2 k + 4 m = -8 Jika dua persamaan tersebut dieliminasi, maka Jika k disubstitusi ke persamaan pertama, maka Sehingga k + m = 2 - 1 = 1

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell r with rightwards arrow on top end cell equals cell k a with rightwards arrow on top plus m b with rightwards arrow on top end cell row cell 7 i with hat on top minus 8 j with hat on top end cell equals cell k open parentheses 3 i with hat on top minus 2 j with hat on top close parentheses plus m open parentheses negative i with hat on top plus 4 j with hat on top close parentheses end cell row cell 7 i with hat on top minus 8 j with hat on top end cell equals cell open parentheses 3 k i with hat on top minus 2 k j with hat on top close parentheses plus open parentheses negative m i with hat on top plus 4 m j with hat on top close parentheses end cell row cell 7 i with hat on top minus 8 j with hat on top end cell equals cell open parentheses 3 k minus m close parentheses i with hat on top plus open parentheses negative 2 k plus 4 m close parentheses j with hat on top end cell row blank blank blank end table end style 

Sehingga didapatkan dua buah persamaan

3= 7

-2+ 4= -8

Jika dua persamaan tersebut dieliminasi, maka

begin mathsize 14px style table row cell 3 k bond m equals 7 end cell cell open vertical bar cross times 4 close vertical bar end cell cell 12 k minus sign 4 m equals 28 space space space space space space space end cell row cell negative sign 2 k and 4 m equals minus sign 8 end cell cell open vertical bar cross times 1 close vertical bar end cell cell bottom enclose negative sign 2 k and 4 m equals minus sign 8 space space space plus end enclose end cell row cell space space end cell cell space space end cell cell 10 k equals 20 yields k equals 2 end cell end table end style   

Jika k disubstitusi ke persamaan pertama, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 k minus m end cell equals cell 7 space end cell row cell 3 left parenthesis 2 right parenthesis minus m end cell equals cell 7 space end cell row cell 6 minus m end cell equals cell 7 space end cell row m equals cell 6 minus 7 space end cell row m equals cell negative 1 end cell end table end style 

Sehingga

= 2 - 1 = 1

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Diketahui vektor a = ( 3 − 2 ​ ) , b = ( 4 1 ​ ) , dan c = ( − 2 − 1 ​ ) . Jika 2 a − 3 b + k c = ( 0 − 4 ​ ) , dengan k bilangan real, maka nilai adalah ..

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