After an end to colonialism, the common challenges that were faced by countries in the Caribbean, Africa, and Asia are: B. military dictatorships, human rights abuses, economic instability.
<h3>What is colonialism?</h3>
Colonialism can be defined as a practice or an act of political and economic domination by a group of people or power from one country over other people or geographical regions that are located in another country, especially by establishing colonies.
Historically, some of the common challenges that that were faced or experienced by countries in the Caribbean, Africa, and Asia faced after an end to colonialism include the following:
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Have you ever done community service or helped lead a big project? Even just some nice things you've done for your school.
The impact of feudalism on American exploration is that Feudalism was said to be a system that brought about local administrative control and the also the sharing of land into units.
<h3>What was the impact of the feudal system?</h3>
The effect of the feudal system was that It brought about the formation of a well localized groups of communities that is said to be owed loyalty to a given local lord who is known to often exercised total authority in his domain.
The Age of Exploration is known to be due to the effect of ideas, technology, plants, and also that of animals that are said to be exchanged all over the world. The Age of Exploration is known to be a factor that lead to the origins of modern capitalism.
Hence, The impact of feudalism on American exploration is that Feudalism was said to be a system that brought about local administrative control and the also the sharing of land into units.
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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.
