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## Main Question or Discussion Point

The question is: are x and ix linearly dependent or independent?

My first guess is that they should be linearly dependent since i is a constant.

But when you apply the definition of linear independence i.e. when you solve ax+ibx=0 (where x≠0), you get a=-ib which shows that the only solution can be a,b=0.

Hence, according to definition of linear independence, x and ix should be linearly independent.

Am I correct?

My first guess is that they should be linearly dependent since i is a constant.

But when you apply the definition of linear independence i.e. when you solve ax+ibx=0 (where x≠0), you get a=-ib which shows that the only solution can be a,b=0.

Hence, according to definition of linear independence, x and ix should be linearly independent.

Am I correct?