lecture 1 - vectors

Question 1

What is sum of vectors?

Answer 1

for a = ( a1,a2,…,an) and b = (b1,b2,..,b2):
a = (a1 + b1, a2 + b2, … an + bn)

Question 2

What is scalar multiplication of vectors?

Answer 2

For Lambda is element of real numbers and a = ( a1,a2,…,an), scalar multiplication = (lambda a1, lambda a2, lambda an)

Question 3

What is scalar product?

Answer 3

the sum of products of each pair between two vectors A and B.
(a1 * b1) + (a2 * b2) + … + (an * bn)

Question 4

What is linear dependency?

Answer 4

2+ vectors are linearly dependent if they can be used to represent the null vector using non-scalars without being zero.
e.g. if R1 + 2(R2) = R3 then they are linearly dependent.

Question 5

What is a null vector?

Answer 5

all elements are 0
A = (0, 0, 0)