Question

Let R*= R\ {0} be the set of nonzero real numbers. Let G= {2x2 matrix: row...

Let R*= R\ {0} be the set of nonzero real numbers. Let

G= {2x2 matrix: row 1(a b) row 2 (0 a) | a in R*, b in R}

(a) Prove that G is a subgroup of GL(2,R)

(b) Prove that G is Abelian

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let G be the set of all 2x2 matrices [a a a a] such that a...
Let G be the set of all 2x2 matrices [a a a a] such that a is in the reals and a does not equal 0. Prove or disprove that G is a group under matrix multiplication.
Let R be a relation on set RxR of ordered pairs of real numbers such that...
Let R be a relation on set RxR of ordered pairs of real numbers such that (a,b)R(c,d) if a+d=b+c. Prove that R is an equivalence relation and find equivalence class [(0,b)]R
1. Let A be the 2x2 matrix in M_{2x2}(C), whose first row is (0,1) and second...
1. Let A be the 2x2 matrix in M_{2x2}(C), whose first row is (0,1) and second row is (-1,0). (a) Show that A is normal. (b) Find (complex) eigenvalues of A. (c) Find an orthogonal basis for C^2, which consists of eigenvectors of A. (d) Find an orthonormal basis for C^2, which consists of eigenvectors of A.
Prove or disprove: GL2(R), the set of invertible 2x2 matrices, with operations of matrix addition and...
Prove or disprove: GL2(R), the set of invertible 2x2 matrices, with operations of matrix addition and matrix multiplication is a ring. Prove or disprove: (Z5,+, .), the set of invertible 2x2 matrices, with operations of matrix addition and matrix multiplication is a ring.
8. Let A = {fm,b : R → R | m not equal 0 and fm,b(x)...
8. Let A = {fm,b : R → R | m not equal 0 and fm,b(x) = mx + b, m, b ∈ R} be the group of affine functions. Consider (set of 2 x 2 matrices) B = {[ m b 0 1 ] | m, b ∈ R, m not equal 0} as a subgroup of GL2(R) where R is the field of real numbers.. Prove that A and B are isomorphic groups.
Let G be an Abelian group. Let k ∈ Z be nonzero. Define φ : G...
Let G be an Abelian group. Let k ∈ Z be nonzero. Define φ : G → G by φ(x) = x^ k . (a) Prove that φ is a group homomorphism. (b) Assume that G is finite and |G| is relatively prime to k. Prove that Ker φ = {e}.
Let E⊆R (R: The set of all real numbers) Prove that E is sequentially compact if...
Let E⊆R (R: The set of all real numbers) Prove that E is sequentially compact if and only if E is compact
For which subspaces S in R^2 is there a 2x2 matrix A for which row(A)=col(A)=S?
For which subspaces S in R^2 is there a 2x2 matrix A for which row(A)=col(A)=S?
Prove: Let S be a bounded set of real numbers and let a > 0. Define...
Prove: Let S be a bounded set of real numbers and let a > 0. Define aS = {as : s ∈ S}. Show that inf(aS) = a*inf(S).
Find an example of a nonzero, non-Invertible 2x2 matrix A and a linearly independent set {V,W}...
Find an example of a nonzero, non-Invertible 2x2 matrix A and a linearly independent set {V,W} of two, distinct non-zero vectors in R2 such that {AV,AW} are distinct, nonzero and linearly dependent. verify the matrix A in non-invertible, verify the set {V,W} is linearly independent and verify the set {AV,AW} is linearly dependent