Solution. To check whether the vectors are linearly independent, we must answer the following question: if a linear combination of the vectors is the zero vector, is it necessarily true that all the coefficients are zeros?
Suppose that
x 1 ⃗v 1 + x 2 ⃗v 2 + x 3 ( ⃗v 1 + ⃗v 2 + ⃗v 3 ) = ⃗0
(a linear combination of the vectors is the zero vector). Is it necessarily true that x1 =x2 =x3 =0?
We have
x1⃗v1 + x2⃗v2 + x3(⃗v1 + ⃗v2 + ⃗v3) = x1⃗v1 + x2⃗v2 + x3⃗v1 + x3⃗v2 + x3⃗v3
=(x1 + x3)⃗v1 + (x2 + x3)⃗v2 + x3⃗v3 = ⃗0.
Since ⃗v1, ⃗v2, and ⃗v3 are linearly independent, we must have the coeffi-
cients of the linear combination equal to 0, that is, we must have
x1 + x3 = 0 x2 + x3 = 0 ,
x3 = 0
from which it follows that we must have x1 = x2 = x3 = 0. Hence the
vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
Answer. The vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
Answer: 1.9%
Explanation:
First derive the Market return as this is needed in the Capital Asset Pricing Model by using the same model:
Required return = Risk free rate + Beta * ( market return - Risk free rate)
Using stock Y:
12.4% = Risk free rate + 1 * (market return - Risk free rate)
12.4% = Rf + market return - Rf
Market return = 12.4%
Use this to calculate the Risk free rate:
Stock Z:
8.2% = Rf + 0.6 * (12.4% - Rf)
8.2% = Rf + 7.44% - 0.6Rf
Rf - 0.6Rf = 8.2% - 7.44%
0.4Rf = 0.76%
Rf = 0.76% / 0.4
= 1.9%
I have the first 3 answers for you but I going to try to get the 4 answer for you
1. 39
2. 9
3. 62
Answer:
D: the globalization of consumer culture.
Explanation:
Answer:
8.6 km/hr
Explanation:
It looks like there's a lot of extra information here. If the question only asks about the trip from Rohn to Nikolai, then the only information that matters is that the distance between the two is 121 km & that Seavey did it in 14 hours. Don't let the extra numbers throw you off.
As for the math behind this - km/hr is a math equation in and of itself. Any ratio like that is a simple division problem. Just plug your numbers (121 km / 14 hr) into the formula (km / hr) to get your answer!
EDIT: for future questions where they don't label it as clearly... velocity = the distance divided by the time.
