Not necessarily.

and

may be linearly dependent, so that their span forms a subspace of

that does not contain every vector in

.
For example, we could have

and

. Any vector

of the form

, where

, is impossible to obtain as a linear combination of these

and

, since

unless

and

.
Answer:
Step-by-step explanation:
Given that among 500 freshmen pursuing a business degree at a university, 315 are enrolled in an economics course, 213 are enrolled in a mathematics course, and 123 are enrolled in both an economics and a mathematics course.
From the above we find that
a) either economics of Math course is

Out of 500 students 405 have taken either Math or Economics
Hence
c) student who have taken neither = 
Exactly one course is either math or economics - both
= 
Answer:
this question is not complete. need another equation
Step-by-step explanation:
give another equation then I can solve

Answer:
vb n bf dgmhumrynwtfvt
Step-by-step explanation:
vb hgetyhrtewr34y4j4htredwed5g