John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Abstract Algebra

Binary Operations In Mathematics: Definition, Examples, And Applications

Binary operation (on a set G) for all a,b in G, a*b in G In mathematics, a binary operation on a set G is a mathematical operation...

John Rhodes
June 21, 2023
Abstract Algebra

The Fundamental Axioms And Properties Of Groups In Mathematics

Axioms of a Group (1) Closure(2)Associativity(3)Identity(4)Inverse A group is a mathematical structure consisting of a set G together with a binary operation * that satisfies certain axioms....

John Rhodes
June 21, 2023
Abstract Algebra

The Identity Axiom: Exploring The Fundamental Concept Of Math

Identity Axiom There exists an element e in G called an identity of G such that for all a in G we have that ae=ea=a The identity...

John Rhodes
June 21, 2023
Linear Algebra

Matrix Multiplication: Debunking The False Claim That Ab = [A1B1 A2B2] For 2 X 2 Matrices A And B.

If A and B are 2 x 2 with columns a1, a2 and b1, b2, respectively, then AB = [a1b1 a2b2]. False because it violates the definition...

John Rhodes
June 21, 2023
Linear Algebra

The True Statement About Matrix Multiplication: Columns Of Ab As Linear Combinations Of Columns Of B Using Weights From Corresponding Columns Of A.

Each column of AB is a linear combination of the columns of B using weights from the corresponding column of A. False because the roles of A...

John Rhodes
June 21, 2023
Linear Algebra

Mastering Matrix Mathematics: The Distributive Property Of Matrix Multiplication Over Addition.

AB + AC = A(B + C) True because this is the distributive property for matrices A, B, and C also mentioned in Theorem 2B. The statement...

John Rhodes
June 21, 2023
Linear Algebra

Matrix Transpose: Proving A^T + B^T = (A + B)^T.

A^T + B^T = (A + B)^T True. See properties of transposition. Also should be able to think through to show this. When we add corresponding entries,...

John Rhodes
June 21, 2023
Linear Algebra

The Transpose Of A Product Rule For Matrices

The transpose of a product of matrices equals the product of their transposes in the same order. False because it should be reverse order not same order....

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