Find the linear map $F : \mathbb{R}^3 → \mathbb{R}^3$ whose image is a subspace with the basis: $\{(1,2,3),(4,5,6)\}$.
2026-04-06 01:20:25.1775438425
How can I find the Linear Map given the Image?
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As has been pointed out in the comments, there are many such maps. So I'm guessing you just want to find one of them.
A linear map is determined by its action on a basis, e.g. the standard basis $\{e_1,e_2,e_3\}$. So what would be a good choice for $F(e_1),F(e_2)$, and $F(e_3)$?