# Vector equation

Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent

Result

c1 = (Correct answer is: ) c2 = (Correct answer is: 2 c1) c3 = (Correct answer is: -c1) #### Solution:

$c_{1} \cdot \ 1+c_{2} \cdot \ 0+c_{3} \cdot \ 1=0 \ \\ c_{1} \cdot \ 2+c_{2} \cdot \ (-1)+c_{3} \cdot \ 0=0 \ \\ c_{1} \cdot \ 1+c_{2} \cdot \ 3+c_{3} \cdot \ 7=0 \ \\ \ \\ c_{1} + c_{3}=0 \ \\ 2 \ c_{1} - c_{2}=0 \ \\ c_{1} + 3 \ c_{2} + 7 \ c_{3}=0 \ \\ \ \\ c_{1}=any \ \\ c_{2}=2 \ c_{1} \ \\ c_{3}=-c_{1}$
$c_{2}=2 \ c_{1}$
$c_{3}=-c_{1}$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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c1 = (Correct answer is: ) OK Tips to related online calculators
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