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 c1−c2=0 c1+3 c2+7 c3=0  c1=any c2=2 c1 c3=−c1
c2=2 c1
c3=−c1c_{3}=-c_{1}

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Showing 2 comments:
#
Matematik
linearly independent

#
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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