Chapter 1. Flashcards
What’s the first property for a matrix to be considered in echelon form?
All nonzero rows are above any rows of all zeros.
What’s the second property for a matrix to be considered in echelon form?
For each row, the leading nonzero entry is in a column to the right of the above row’s leading nonzero entry.
What is the third property for a matrix to be in echelon form?
All entries in a column below a leading nonzero entry are zeros.
What is the first property for a matrix to be considered in reduced echelon form?
Each leading entry of a column is a 1.
What is the second property for a matrix to be in reduced echelon form?
Each leading entry is only nonzero entry in its column.
Do we want echelon form or reduced echelon form?
Echelon form requires less work but the solution is not as obvious. Reduced echelon form requires more work but however the solution to the system is more clear.
What is a pivot position?
A column with a leading entry.
What is a pivot column?
A column that has a pivot position nested in it.
What is a basic variable?
Corresponds to value that, represents a pivot position in the matrix.
What is a free variable?
Value that is nested inside of a non-pivot column.
What happens when the echelon form of a matrix contains a row of the form: [0 0 0 0 … | != 0]?
We would say that there is no solution.
When is a solution unique to a system?
A solution is unique whenever there are no free variables and there are only basic variables.
When does a system in echelon form have an infinite amount of solutions?
A system in echelon form has an infinite amount of solutions, whenever we have free variables inside of the matrix.
What is linear algebra?
This would be the study of system of linear equations.
What is a linear equation?
An equation of the form: a_1x_1 + a_2x_2 + … + a_nx_n = b
