Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Why Multiplying A Rational Number With An Irrational Number Always Results In An Irrational Number: A Simple Proof By Contradiction

product of rational number and irrational number is irrational an irrational number. When we multiply a rational number (a number that can be expressed in the form...

John Rhodes
June 21, 2023
Calculus

Proving The Irrationality Of The Sum And Product Of Two Irrational Numbers

sum or product of two irrational numbers is rational or irrational g enerally irrational. Proof: Let a and b be two irrational numbers. We assume that their...

John Rhodes
June 21, 2023
Calculus

Discover The Importance And Applications Of Natural Numbers In Mathematics

natural numbers 1, 2, 3, 4, 5, … Natural numbers are the set of positive integers (whole numbers) such as 1, 2, 3, 4, 5, 6, 7,...

John Rhodes
June 21, 2023
Calculus

Composite Numbers: The Key Role They Play In Algebraic Equations, Number Theory And Security

composite numbers are positive and not prime Composite numbers are positive integers that have more than two factors (divisors). In other words, a composite number is a...

John Rhodes
June 21, 2023
Calculus

The Fundamental Theorem Of Algebra: Guaranteeing A Complex Solution To Every Polynomial Equation

the fundamental theorem of algebra any polynomial with complex coefficients has at least one complex root The fundamental theorem of algebra is a theorem in mathematics that...

John Rhodes
June 21, 2023
Calculus

The Properties Of Matrix Multiplication For Square Matrices In Math.

Is matrix multiplication for square matrices commutative, associative, or distributive? only associative and distributive Matrix multiplication for square matrices is associative but not commutative or distributive. Associativity...

John Rhodes
June 21, 2023
Calculus

Discovering The Conditions For A Square Matrix To Have An Inverse: From Determinants To Linear Independence

a square matrix has an inverse iff the determinant is nonzero There are different ways to state the conditions for a square matrix to have an inverse,...

John Rhodes
June 21, 2023
Calculus

Mastering The Dot Product Of Matrices: A Comprehensive Guide For Linear Algebra And Machine Learning

dot product of a matrix must have (m n) (n y)multiply row by column The dot product of two matrices is an operation that results in a...