Miscellaneous

Question 0

Number of Parameter

Answer 0

Number of columns - rank

Question 1

Rank

Answer 1

Number of leading ones

Question 2

Homogeneous System of Linear Equations

Answer 2

• system that is equal to zero

- always have at least one solution (trivial: all zeros)

Question 3

Goal: Homogeneous Systems

Answer 3

• find a non-trivial solution

- must have at least one parameter (rank < m)

Question 4

Basic Solution

Answer 4

• set one parameter to one and the others to zero

Question 5

Number of Basic Solutions

Answer 5

number of columns - rank

ex. sX1 + tX2 (2 basic solutions)

Question 6

Linear Combinations

Answer 6

• shows all possible solutions

- sum of the multiples of basic solutions

Question 7

General Systems

Answer 7

• solution to the homogenous solution (X0) + solution to original system = new solution