Linear Algebra | Senioritis

John Rhodes
June 21, 2023
Linear Algebra

How to Solve a Linear System Using Substitution or Elimination Method

The solution set of the linear system… is the set of all possible solutions. In order to find the solution set of a linear system, we need...

John Rhodes
June 21, 2023
Linear Algebra

Understanding Linear Systems Equivalence with Gaussian Elimination and Row Operations

When are two linear systems called equivalent? If they have the same solution set. Two linear systems are called equivalent if they have the same solution set....

John Rhodes
June 21, 2023
Linear Algebra

Ensuring Consistency in Mathematical Systems: Why It Matters

When is a system consistent? When it has either exactly one solution or infinitely many solutions. A system is consistent when all the equations and constraints in...

John Rhodes
June 21, 2023
Linear Algebra

Understanding Inconsistent Systems in Mathematics: Definition and Examples

When is a system inconsistent? When it has no solution. A system is inconsistent when it cannot have a solution that satisfies all of its equations or...

John Rhodes
June 21, 2023
Linear Algebra

Unlocking the Solutions: Understanding the Importance and Applications of Coefficient Matrices in Linear Equations and Beyond

What is a coefficient matrix? The matrix with the coefficients aligned in columns. A coefficient matrix is a square or rectangular matrix that shows the coefficients of...

John Rhodes
June 21, 2023
Linear Algebra

Solving Linear Equations: Understanding Augmented Matrix and Row Reduction Operations.

What is an augmented matrix? Consists of the coefficient matrix with an added column containing the constants from the right sides of the equations. An augmented matrix...

John Rhodes
June 21, 2023
Linear Algebra

Mastering Matrix Notation: Understanding Rows and Columns in a 3×4 Matrix

In a 3 x 4 matrix, the rows are _ and the columns are _. Rows are represented by 3, columns by 4. In a 3 x...

John Rhodes
June 21, 2023
Linear Algebra

Master the Basics: Understanding Linear Equations and their Applications

linear equation in the variable x1,…,xn is an equation that can be written in the form a1x1+…+anxn = b where b and the coefficients a1,..,an are all...