John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Linear Algebra

Matrix Echelon And Reduced Row Echelon Forms For Linear Algebra

When is a matrix in echelon form? Reduced form? 1.) Any and all zero rows are at the bottom.2.) The first non-zero (leading) entry of a row...

John Rhodes
June 21, 2023
Linear Algebra

Everything You Need To Know About Reduced Echelon Form And Row Equivalence Of Matrices In Linear Algebra

True or false: Each matrix is row equivalent to one and only one reduced echelon matrix. 1 True. Every matrix can be row reduced to an echelon...

John Rhodes
June 21, 2023
Linear Algebra

Pivot Positions And Pivot Columns In Linear Algebra For Solving Systems Of Equations

What is a pivot position? Pivot column? A pivot position in a matrix A is a location in A that corresponds to a leading 1 in the...

John Rhodes
June 21, 2023
Linear Algebra

A Guide To Pivot And Free Variables In Linear Programming For Optimal Solutions

What is a pivot/basic variable? Free variable? A pivot/basic variable corresponds to a pivot column. A free variable corresponds to a solution of the system for any...

John Rhodes
June 21, 2023
Differential Equations

Mastering The Power Of The Existence And Uniqueness Theorem For Differential Equations In Mathematics

Existence and Uniqueness Theorem a linear system is consistent if and only if the rightmost column of the augmented matrix is NOT a pivot column – that...

John Rhodes
June 21, 2023
Arithmetic

Mastering The Basics Of Arithmetic Sequences: Formulas, Applications, And Examples

Arithmetic sequence a sequence in which each term is found by adding the same number to the previous term An arithmetic sequence is a sequence of numbers...

John Rhodes
June 21, 2023
Arithmetic

Mastering Geometric Sequences: Definition, Formula, And Real-Life Applications

geometric sequence a sequence in which each term is found by multiplying the previous term by the same numbers A geometric sequence, also known as a geometric...

John Rhodes
June 21, 2023
Arithmetic

How To Find Any Term In A Geometric Sequence With The Formula A(N) = A(1) * R^(N-1)

Formula for geometric sequence an=a1(r)^n-1*use formula to sub for n The formula for a geometric sequence is: a(n) = a(1) * r^(n-1) where: a(n) is the nth...

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