# 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:

$c_{1} \cdot \ 1+c_{2} \cdot \ 0+c_{3} \cdot \ 1=0 \ \\ c_{1} \cdot \ 2+c_{2} \cdot \ (-1)+c_{3} \cdot \ 0=0 \ \\ c_{1} \cdot \ 1+c_{2} \cdot \ 3+c_{3} \cdot \ 7=0 \ \\ \ \\ c_{1} + c_{3}=0 \ \\ 2 \ c_{1} - c_{2}=0 \ \\ c_{1} + 3 \ c_{2} + 7 \ c_{3}=0 \ \\ \ \\ c_{1}=any \ \\ c_{2}=2 \ c_{1} \ \\ c_{1}=c_{3}=-c_{1}$
$c_{2}=2 \ c_{1}$
$c_{3}=-c_{1}$

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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Matematik
linearly independent

Math student
c1 = (Correct answer is: ) OK

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