math

Question 1

what is a vector space

Answer 1

a set of vectors closed under addition and multiplication that satisfy properties like communitive, associative, and distributive laws

Question 2

what is algebra

Answer 2

the study of sets along with operations

Question 3

what is a linear combination

Answer 3

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.

Question 4

what is a subspace

Answer 4

a subspace is a subset of a vector space that is closed under addition and scalar multiplication + contains the zero vector.

Question 5

What does it mean for a set of vectors to be linearly independent

Answer 5

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

Question 6

What is a basis for a subspace

Answer 6

A set is a basis of a subspace if:
1) the set is linearly independent
2) the span of the set produces the subspace

Question 7

what are the three possible outcome when solving a system of linear equation

Answer 7

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