Week 9 Flashcards
(7 cards)
1
Q
Subspace Criterion?
A
- Must be non empty (Contains the zero vector:)
-Closed under addition.
-Closed under scalar multiplication
1
Q
How to do scalar addition for sub criterion?
A
-use normal function and just use two variables for one and see if you get same form
so u + v (x)
2
Q
How to do scalar multiplication for sub criterion?
A
multiply constants by lambda , divide lambda out then we have λf(x)
if =0 we can show λf(x) = λ(0)=0
or just show λf(x)= λa …… where λa and λb E R,
3
Q
How can we show a linear span (vectors of a matrix) spans R^n?
A
-If the matrix has full row rank
4
Q
How can we show a linear span (vectors of a matrix) does not span R^n?
A
-If the matrix does not have full row rank
5
Q
How can we show a linear span (vectors of a matrix) is linearly independent?
A
- has full column rank
6
Q
How can we show a linear span (vectors of a matrix) is linearly dependent?
A
- does not have full column rank
