deck_15039904 Flashcards
Vector
An ordered list of numbers, a matrix with one column
R
Real numbers
Zero vector
A vector of all zeros, origin
Vector Addition
[a + [c. = [a +cb]. a] b + b]
Scalar Multiplication
k [a. = [k x a b] k x b ]
What does multiplication do to vectors?
Lengthens them
What does scaling by a negative factor do?
Changes the direction of the vector
Linear Combination
Combining vectors with addition and scalar multiplication
Span
The set of all linear combinations of vectors
How do you read vectors?
Column by column
1 independent vector
line in r^3
2 independent vectors
plane in r^3
3 independent vectors
all of r^3
Linearly Dependent
A set of vectors where one or more vectors already lie in the span of the other vectors
Linear Dependence in r^2
If you have one or more vectors in r^2 then they must be linearly dependent
What if there is a zero vector in span?
It will always be linearly dependent since the 0 vector is in all spans
How do you tell if vectors are linearly dependent or independent?
Check if C1V1 + C2V2…CkVk = 0 is true for all coeff other than all 0’s
How to list the 5 vectors in a span
vector 1: 0v1 + 0v2vector 2: 1v1 + 0v2vector 3: 0v1 + 1v2vector 4: 1v1 + 1v2vector 5: 2v1 + 1v2
