We are approaching complex numbers and complex spaces and I am confused with both of them and their relationship to linear algebra. I have a question from a lecture slide: Working in C^3, determine if (1,2,0) is in span((i,0,0),(i,i,0),(i,i,i)). There is a tip to set (1,2,0) equal to the span, but I am not sure if I'm to make an augmented matrix from there or what.
2026-03-28 12:34:07.1774701247
Determine if (1,2,0) is in the Span
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Guide:
Assuming your field is $\mathbb{C}$, the question is asking if you can find $a,b,c \in \mathbb{C}$ such that $$a(i,0,0)+b(i,i,0)+c(i,i,i) = (1,2,0)$$
You might like to determine what is $c$ first by comparing the third component, then determine $b$ and $a$.