John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Linear Algebra

Understanding Matrix Size: The Relationship Between Rows and Columns Explained with m*n Notation

The size of a matrix is given as m*n, where m is the number of __________ and n is the number of ___________ Rows; columns The size...

John Rhodes
June 21, 2023
Linear Algebra

Understanding Row Equivalence and Elementary Row Operations for Math Equations

What makes 2 equations row equivalent? If there is a series of elementary row operations that transforms one matrix into the other Two equations are said to...

John Rhodes
June 21, 2023
Linear Algebra

The Row Equivalence Theorem: Simplify Calculations in Linear Systems by Understanding Row Equivalence

If the augmented matrices of two linear systems are row equivalent… The 2 systems have the same solution set If the augmented matrices of two linear systems...

John Rhodes
June 21, 2023
Linear Algebra

Master the Basics: Understanding Echelon and Reduced Row Echelon Form in Matrices

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

Matrix Row Operations: Unique Path to Reduced Echelon Form.

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

John Rhodes
June 21, 2023
Linear Algebra

Pivot Columns and Positions in Linear Algebra: Importance in Matrix Reduction and Equation Solving

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

Understanding Pivot and Free Variables in Linear Programming

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

Understanding the Existence and Uniqueness Theorem for Differential Equations

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...