Mathematics | Senioritis

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...

John Rhodes
June 21, 2023
Calculus

Learn How to Reflect and Translate Points on the Coordinate Plane with Math Examples

Reflect over x-axis; translate left 2 y = -(x + 2)² To reflect a point, line, or shape over the x-axis, we simply reverse the sign of...

John Rhodes
June 21, 2023
Calculus

Mastering Reflection across the X-Axis: A Guide to Flipping Math Figures with Ease.

reflection across the x-axis f(x) = – (x³) Reflection across the x-axis is a transformation in which each point in a figure is flipped or reflected over...

John Rhodes
June 21, 2023
Calculus

Mastering Math: Subtracting Outside the Function for Function Output Modification

Subtracting outside the function f(x) = x² – c or (x)² – c where c is any number. Subtracting outside the function means subtracting a constant value...