What is Gaussian elimination?
Q: What is Gaussian elimination?
A: Gaussian elimination is a method used in mathematics to solve systems of linear equations.
Q: Who is it named after?
A: It is named after Carl Friedrich Gauss, a famous German mathematician who wrote about this method, but did not invent it.
Q: How is Gaussian elimination performed?
A: Gaussian elimination is performed by using the coefficients of the terms in the system of linear equations to create an augmented matrix. Then, elementary row operations are used to simplify the matrix.
Q: What are the three types of row operations used in Gaussian elimination?
A: The three types of row operations used in Gaussian elimination are: Switching one row with another row, Multiplying a row by a non-zero number, and Adding or subtracting a row from another row.
Q: What is the goal of Gaussian elimination?
A: The goal of Gaussian elimination is to get the matrix in row-echelon form.
Q: What is row-echelon form?
A: If a matrix is in row-echelon form, that means that reading from left to right, each row will start with at least one more zero term than the row above it.
Q: What is reduced row-echelon form?
A: Reduced row-echelon form means that the matrix is in row-echelon form and the only non-zero term in each row is 1. Gaussian elimination that creates a reduced row-echelon matrix result is sometimes called Gauss-Jordan elimination.
