John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Trigonometry

The Equation X^2 + Y^2 = R^2 And Its Representation Of A Circle On A Cartesian Coordinate System

x^2 + y^2 = r^2 equation of a circle centered at (0, 0) with the radius r The equation x^2 + y^2 = r^2 represents a circle...

John Rhodes
June 21, 2023
Linear Algebra

Solving Systems Of Equations With Three Variables: Elimination And Matrix Methods

What are the solution sets for equations with 3 variables? Set of Intersections of the Planes:1.) Line 2.) Point 3.) Nothing The solution sets for equations with...

John Rhodes
June 21, 2023
Linear Algebra

Consistent And Inconsistent Systems Of Equations In Math

What makes a system consistent? Inconsistent? Consistent if there is at least 1 solution (there can be infinite) Inconsistent if there is no solution A system of...

John Rhodes
June 21, 2023
Linear Algebra

Matrix Size: Explaining M*N Notation For Rows And Columns

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

Row Equivalence In Linear Equations: Elementary Row Operations Explained

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 row equivalent...

John Rhodes
June 21, 2023
Linear Algebra

Mathematical Equivalence Of Linear Systems: How Row Equivalence Between Augmented Matrices Ensures Same Solutions

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

Matrix Echelon And Reduced Echelon Form For Efficient Algebraic Operations

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

Row Operations And Reduced Echelon Matrices: A Comprehensive Guide

True or false: Each matrix is row equivalent to one and only one reduced echelon matrix. 1 True. Row operations are reversible, and each row operation can...