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.
Software development. A software developer designs and creates tech which can be used for multiple purposes, both creative, practical and for entertainment purposes. A digital music manager would fall into the category of being some software in which a user could develop a method to manage music.
The given situation represents the example of a clinical/case study of the research method.
<h3>What is a clinical/case study?</h3>
A clinical case study refers to the case study where the doctors share the cases of patients that are not common or not explained before. In this, the permission of the patient should be required for writing the report on the clinical case.
Hence, we can conclude that The given situation represents the example of a clinical/case study of research method.
Learn more about research here: brainly.com/question/16778033
B. Weakened
Overtiredness has a negative effect on driving capabilities.
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The purpose of accreditation<span> is the improvement of academic quality and public accountability.</span>
