Semaine 1 Flashcards
Hw many solution can a linear system have?
Three.
Unique solution
Infinite solution
no solutions
What are the different elementary. rows operations?
Replacement
interchange
Scaling
What’s a consistent system?
A system that has one or infinite solution
What’s a consistent system?
A system that has no solution
When do we know that a system has an unique solution
When there’s a pivot in each column
What are the addition vectors properties?
Commutative a+b = b+a
Associative a+(b+c)=(a+b)+c
Zero vector u+0=u
the zero vector u+(-u)=0
What are the addition vectors properties?
distributive property
c -d are scalars
(a-b are vectors)
a(c+d)=(ab)+(ad)
c(a+b)=ac+ab
What are the addition vectors properties?
Commutative
a+b = b+a
What are the addition vectors properties?
Associative
a+(b+c)=(a+b)+c
What are the addition vectors properties?
Zero vector
u+0=u
What is a linear combinations
when we can multiple two or more vectors to get a new one
What is a span of a set of vector span{u,v}
the sets of all vectors generated by u and v
When does a linear combination generated b
When there’s an unique solution to the linear system
Which vectors is always in span
the zero vectors always in span
