math Flashcards
what is a vector space
a set of vectors closed under addition and multiplication that satisfy properties like communitive, associative, and distributive laws
what is algebra
the study of sets along with operations
what is a linear combination
Let V1,V2, . . Vp be in R^n
let C1,V2, . . .Cp be in R
the vector C1V1+C2V2 . . . CpVp is called a linear combination of those vectors.
what is a subspace
a subspace is a subset of a vector space that is closed under addition and scalar multiplication + contains the zero vector.
What does it mean for a set of vectors to be linearly independent
A set of vectors are linearly independent if there is no linear combination that can make the set equal to zero, except if all the weights are set to zero
What is a basis for a subspace
A set is a basis of a subspace if:
1) the set is linearly independent
2) the span of the set produces the subspace
what are the three possible outcome when solving a system of linear equation
either there is a unique solution, infinitely many solutions, or no solutions.
A system that has a unique/infinite solutions, it is called a consistent system.
If there are no solutions, it is called an inconsistent system
