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: ) OK
c2 = (Correct answer is: 2 c1) Wrong answer
c3 = (Correct answer is: -c1) Wrong answer

Solution:

c1 1+c2 0+c3 1=0 c1 2+c2 (1)+c3 0=0 c1 1+c2 3+c3 7=0  c1+c3=0 2 c1c2=0 c1+3 c2+7 c3=0  c1=any c2=2 c1 c1=c3=c1c_{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}
c2=2 c1c_{2}=2 \ c_{1}
c3=c1c_{3}=-c_{1}



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Matematik
linearly independent

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Math student
c1 = (Correct answer is: ) OK
c2 = (Correct answer is: 2 c1) Wrong answer
c3 = (Correct answer is: -c1) Wrong answer

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