Uniquely determined proof

Related BrainMass Solutions

• Fields and homomorphisms

  (b) From the proof in (a), we know that any -algebra homomorphism is uniquely determined by . Assume , then for any , we have Since is a -algebra homomorphism, we have So is uniquely determined by .

• Determinant function proof

  177955 Determinant Function Proof Please see the attached file. Please kindly show each step of your solution. Without using Proposition 2.6, prove that the determinant function is uniquely determined by the properties listed...

• Algebra: fraction decomposition

  For example, if we trz a decomposition of: Where x = a and and where x = b and and where x = c and As we could see, since l,m and n on the numerator as well as a,b and c on the denominator are uniquely determined, then A, B and C are uniquely

• Denote the vector space of all nxn matrices

  Moreover, because , then any symmetric matrix is uniquely determined by its upper triangle entries. So the dimension of is . Done. The expert examines denoting the vector space of all nxm matrices.

• Mobius Transformations for Circles

  If a,b,c are any 3 points on R and we can specify T(a), T(b), T(c), then such a T is uniquely determined. (Conway says that this proof is trivial, and we may use the fact that M-maps take circles onto circles).

• Square roots of prime numbers

  This is a proof regarding the square root of a prime number.

• Z-Modules and Isomorphisms

  So each homomorphism f from Z/nZ to Z/mZ is uniquely determined by f(1). Let f_k in Hom_Z(Z/nZ,Z/mZ) denote the homomorphism such that f_k(1)=k mod m. Since 0=f_k(0)=f_k(n)=nf_k(1)=nk, then nk=0 mod m. so m|nk.

• Advantages of a database over electronic files to store data

  The advantages of a database over electronic files to store data are determined. The expert explains the concept of a primary key in a relational table are determined.

• Proof using The Euler Function and Fermat's Theorem

  Now I am going to give you a proof. Proof.