Base: $$((1,0,2), (2,1,1), (1,1,1)) $$ I found out, all of vectors are linear independent. So it creates base of $\mathbb Q^3$. So I need to put this vector: $$(3,2,-3) $$ And put this vector to the base. How can I put in? I know I can have only 3 vectors. So can I just replace vectors? Or there is some methods to do it?
2026-03-30 05:31:57.1774848717
Put a vector to base of Vectors in Rational number
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Take the matrix $A$ which has given basis vectors as column and solve the system
$$Ax=\begin{pmatrix}3\\2\\-3\end{pmatrix}$$
which has an unique solution.