Question

niech wektor a = [2, 3] b= -4, 1] c = [0, 7] dobierz liczby k i l tak aby k*a+l*b=c

Answer 1

 a = [2, 3] b= -4, 1] c = [0, 7]

 

 k* [2, 3 ] + l * [ -4, 1 ] = [0, 7]

  

k * 2 + l * (-4) = 0

k * 3 + l * 1 = 7

 

2k - 4l = 0

3k + l = 7    / * 4

 

2k - 4l = 0

12k + 4l = 28

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14k = 28

k = 2

 

3k + l = 7

6 + l = 7

l = 1

 

odp. k = 2,  l = 1  

Answer 2

 

a  = [ 2; 3 ]

b = [ - 4; 1 ]

c = [ 0; 7]

zatem

k*a + l*b = k*[ 2; 3] | l*[ - 4; 1] = [ 2k ; 3 k] + [ - 4 l; 1 l ] = [ 2 k - 4 l;  3 k + 1 l ] = c

czyli

[ 2 k - 4 l; 3 k + 1 l ] = [ 0; 7 ]

Mamy więc

2 k - 4 l = 0

3 k + 1 l = 7 => l = 7 - 3 k

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2 k - 4*( 7 - 3 k ) = 0

2 k - 28 + 12 k = 0

14 k = 28

k = 2

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 l = 7 - 3*2 = 7 - 6 = 1

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Odp. k = 2,  l = 1

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