Linear Algebra | 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
Linear Algebra

Mastering Linear Equations: A Fundamental Tool in Math, Physics, Economics and More

Linear Equation Definition in the variables x1,x2,xn is an equation that can be written in the form a1x1 + a2x2 + anxn = b A linear equation...

John Rhodes
June 21, 2023
Linear Algebra

Mastering System of Linear Equations: Solving with Substitution and Elimination Methods.

System of Linear Equations is a collection of 1 or more linear equations involving the same variables A system of linear equations is a set of two...

John Rhodes
June 21, 2023
Linear Algebra

Mastering the Basics: Understanding Solution Sets in Math Equations and Inequalities

Solution Set The set of all solutions to a system A solution set is the set of values that satisfy a given equation or inequality. In the...

John Rhodes
June 21, 2023
Linear Algebra

Mastering the Concept of Equivalence in Mathematics: Simplify and Solve Complex Equations like a Pro

Equivalent Two systems are this if they have the same solution set In mathematics, equivalent means two expressions or equations have the same value or meaning. That...