The triangle ∆ with vertices P = (0, 0), Q = (1, 0), R = (0, 2) is given. 1.Give an affine-linear mapping Ψ ̸= id, which
Posted: Thu Jun 30, 2022 7:37 pm
The triangle ∆ with vertices P = (0, 0), Q = (1, 0), R =(0, 2) is given.
1.Give an affine-linear mapping Ψ ̸= id, which maps delta intoitself, for which Φ(∆) = ∆ holds, explicitly in the form Ψ(x) = Ax+ b!
2.How many mappings with this property are there? Showthat the set of all maps from Part 1 (including the identity) formsa subgroup of the group of bijective, affine-linearmaps.
Hint: Show that an affine linear map Ψ maps ∆ intoitself if and only if Ψ({P, Q, R}) = {P, Q, R}
// I need the answer to the second question.//
1.Give an affine-linear mapping Ψ ̸= id, which maps delta intoitself, for which Φ(∆) = ∆ holds, explicitly in the form Ψ(x) = Ax+ b!
2.How many mappings with this property are there? Showthat the set of all maps from Part 1 (including the identity) formsa subgroup of the group of bijective, affine-linearmaps.
Hint: Show that an affine linear map Ψ maps ∆ intoitself if and only if Ψ({P, Q, R}) = {P, Q, R}
// I need the answer to the second question.//