1. I.10 Linear Spaces

Condition: to prove that the vectors of the species \ (\ left (x_ {1}, x_ {2}, x_ {3}, x_ {4} \ right) \) form a linear subspace in space \ (\ mathb {r} {4} \). Find the basis and dimension of this subspace. Supplement the subspace base to the basis of the entire space. Find the matrix of the transition from the canonical basis of the space \ (\ mathbb {r}^{4} \) to the constructed basis. \ [\ left (x_ {1}, x_ {2}, x_ {3}, x_ {4} \ right) = (a-b+3 c, -2 b, c, a+2 b) \ text {. } \]