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.
The source of pollution in Lake Erle sewage and Phosphate-containing particles. The point source is discharge pipe while the non-point source of pollution are various ways pollutant is been disposed on the lake.
<h3>What is point source and nonpoint source pollution?</h3>
The Point Sources of a Pollution is one that comes from a single and a source that can be identified example is discharge or drainage pipe that takes waste from a factory or sewage plant.
Note that Pollution that does not have a place where it is coming from is known as nonpoint-source pollution such as wind, run off water carrying waste, etc.
Learn more about pollution from
brainly.com/question/24704410
Answer:
Move the decimal point two places to the right to find the product. To multiply a decimal number by a power of ten (such as 10, 100, 1,000, etc.), count the number of zeros in the power of ten. ... The multiplier 100 has two zeros, so you move the decimal point in 0.054 two places to the right—for a product of 5.4.
Explanation:
Thank you for the answer:)
