Week Two System Of Linear Equation

Question 1

What is row echelon form ?

Answer 1

A Matrix form Where the first non-zero entry on a row is to the right of the first non-zero entry on the previous row.

Question 2

What is a pivot?

Answer 2

The pivot or pivot entries of a matrix are the first non zero entries in each row of the matrix.

Question 3

How to get to row echelon form.

Answer 3

Work from top to bottom row using the current row to eliminate entries on the left in all row below if this is not possible swap you rows.

Question 4

What is reduced row echelon form

Answer 4

A matrix of the form in row echelon form pivots are 1 all entries above pivots are 0.
Or
If all the pivots are equal to 1 and the pivots are the only entry in the columns.

Question 5

How to get to reduced row echelon form

Answer 5

Work from the bottom row to the top using the current row ton eliminate entries above all pivots. Divide each row so that the pivots are 1.

Question 6

How do you know if a system is inconsistent ?

Answer 6

If there is a pivot in the final Column
Or the
Rank(A) ≠ (A|B)

Question 7

How do you know if a system is consistent?

Answer 7

There are no pivots in the final column
Or
If
the Rank(A) = (A|B)

Question 8

How do you know a system has a unique solution?

Answer 8

No free variables
Or
Rank = the number of unknown variables

Question 9

How do you know a system has infinitely many solutions

Answer 9

Free variables( parameters) exist.
Or
Rank < number of unknown variables.