2.1 Intro to linear equation systems

Question 1

when is a system of linear eqns called consistent

Answer 1

when it has at least one solution

Question 2

when is a system of LE inconsistent

Answer 2

when it has no solutions

Question 3

a system of LE with real coeffecients has 3 options

Answer 3

1. a unique soln (consistant)
2. infintely many soln( also cosistant)
3. no soln (inconsistant)

Question 4

when do we solve for a specific x and y and when do we just leave answer to system of LE i.t.o t

Answer 4

leave i.t.o when you have a free variable

then express x and y i.t.o t

Question 5

rank of a matrix

Answer 5

the number of non zero rpws in its row echelon form

Question 6

3 things to define reduced row echelon form

Answer 6

• row echelon
• the leading entry in each non zero row is a 1 (leading 1s)
• each column containing a elading 1 has 0 everywhere else

Question 7

When is a system of solutions of LE termed homogenous

Answer 7

THIS IS ONE TYPE OF SYSTEM THAT ALWAYS AHS AT LEAST 1 SOLN

the constant term in each eqn is zero

a homogenous soln has

1. unique soln (the zero soln, or the trivial soln)
2. infinetely many soln (here we need a free variable and express soln i.t.o t )