Let H = {A∈GL(2,R)|(detA)2= 1}. Prove that H / GL(2,R).

Solutions

Expert Solution

Colby Messinger answered 2 years ago

Next > < Previous

Related Solutions

Prove that GL(2, Z2) is a group with matrix multiplication

Let S ⊆ R and let G be an arbitrary isometry of R . Prove that...

Let S ⊆ R and let G be an arbitrary isometry of R . Prove that the symmetry group of G(S) is isomorphic to the symmetry group of S. Hint: If F is a symmetry of S, what is the corresponding symmetry of G(S)?

1. Let A be an inductive subset of R. Prove that {1} ∪ {x + 1...

1. Let A be an inductive subset of R. Prove that {1} ∪ {x + 1 | x ∈ A} is inductive. 2. (a) Let n ∈ N(Natural number) and suppose that k 2 < n < (k + 1)2 for some k ∈ N. Prove that n does not have a square root in N. (b) Let c ∈ R \ {0}. Prove that if c has a square root in Z, then c has a square root in...

Let G, H, K be groups. Prove that if G ≅ H and H ≅ K...

Let G, H, K be groups. Prove that if G ≅ H and H ≅ K then G ≅ K.

Let R be a ring with at least two elements. Prove that M2×2(R)is always a ring...

Let R be a ring with at least two elements. Prove that M2×2(R)is always a ring (with addition and multiplication of matrices deﬁned as usual).

Let f : R → R be a function. (a) Prove that f is continuous on...

Let f : R → R be a function. (a) Prove that f is continuous on R if and only if, for every open set U ⊆ R, the preimage f −1 (U) = {x ∈ R : f(x) ∈ U} is open. (b) Use part (a) to prove that if f is continuous on R, its zero set Z(f) = {x ∈ R : f(x) = 0} is closed.

Let H be the subset of all skew-symmetric matrices in M3x3 a.) prove that H is...

Let H be the subset of all skew-symmetric matrices in M3x3 a.) prove that H is a subspace of M3x3 by checking all three conditions in the definition of subspace. b.) Find a basis for H. Prove that your basis is actually a basis for H by showing it is both linearly independent and spans H. c.) what is the dim(H)

Let R be the real line with the Euclidean topology. (a) Prove that R has a...

Let R be the real line with the Euclidean topology. (a) Prove that R has a countable base for its topology. (b) Prove that every open cover of R has a countable subcover.

Let S ⊆ R be a nonempty compact set and p ∈ R. Prove that there...

Let S ⊆ R be a nonempty compact set and p ∈ R. Prove that there exists a point x_0 ∈ S which is “closest” to p. That is, prove that there exists x0 ∈ S such that |x_0 − p| is minimal.

Let X be a subset of R^n. Prove that the following are equivalent: 1) X is...

Let X be a subset of R^n. Prove that the following are equivalent: 1) X is open in R^n with the Euclidean metric d(x,y) = sqrt((x1 - y1)^2+(x2 - y2)^2+...+(xn - yn)^2) 2) X is open in R^n with the taxicab metric d(x,y)= |x1 - y1|+|x2 - y2|+...+|xn - yn| 3) X is open in R^n with the square metric d(x,y)= max{|x1 - y1|,|x2 - y2|,...,|xn -y n|} (This can be proved by showing the 1 implies 2 implies 3)...

Subjects