MATLAB help finding a set of linearly independent vectors

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SUMMARY

The discussion focuses on determining the conditions for linear independence of the vectors v1 = {-4; 3; -10}, v2 = {2; -2; -3+k}, and v3 = {2; -6; 14} in MATLAB. The key conclusion is that the vectors are linearly independent if and only if k is not equal to a specific value, which can be derived by solving the equation c1*v1 + c2*v2 + c3*v3 = 0 or equivalently Ax = 0. The user encountered difficulties in treating k as a variable in MATLAB, specifically when attempting to use symbolic computation with the 'syms' function.

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If I'm given a set of vectors
{-4; 3; -10} = v1
{2; -2; -3+k} = v2
{2; -6; 14} = v3
I want to find that they are linearly independent if and only if k != something

to solve this is simple but a huge tedious pain (although not nearly as tedious as trying to find a solution to this question)

I just solve:

c1*v1 + c2*v2 + c3*v3 = 0
or
Ax = 0 where a is matrix above

I'm desperately trying to convince MATLAB that k is a variable but can't do it. I've tried making it symbolic with syms but it doesn't work. Please help me. Thank you
 
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You should try expanding all three equations and having symbolic solve them simultaneously rather than using the cell format you have above.
 

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