Week 9

Question 1

What is the zero vector?

Answer 1

For any x , function equals zero when we use this vector, but if this zero vector does not exist then not a subspace

Question 1

Subspace Criterion?

Answer 1

-Contains the zero vector:
-Closed under addition.
-Closed under scalar multiplication

Question 2

How to do scalar addition for sub criterion?

Answer 2

-use normal function and just use two variables for one and see if you get same result

Question 3

How to do scalar multiplication for sub criterion?

Answer 3

-use lambda multiplied by vector and use original equation to get lambda x vector = constant

Question 4

How can we show a linear span (vectors of a matrix) spans R^n?

Answer 4

-If the matrix has full row rank

Question 5

How can we show a linear span (vectors of a matrix) does not span R^n?

Answer 5

-If the matrix does not have full row rank

Question 6

How can we show a linear span (vectors of a matrix) is linearly independent?

Answer 6

• has full column rank

Question 7

How can we show a linear span (vectors of a matrix) is linearly dependent?

Answer 7

• does not have full column rank