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:
It applies only to American cities
Explanation:
Answer:
0.95 kPa
Explanation:
(4.0)(1.9) = (
)(8.0)
kPa
-- However, you should see that when the volume increases (doubles, in this case) you will divide the original pressure value by 2. Pressure and volume are inversely related.
The features of rift valley physiological region are:
- volcanoes,
- hot springs,
- geysers,
- frequent earthquakes.
<h3>What is a Rift Valley?</h3>
This refers to the lowland that is sloped downwards and is caused by a fault in the earth's crust.
Hence, we can see that based on the rift valley physiological region, there is pulling apart of the lithosphere and this is increased through the presence of erosion and the features are listed above.
Read more about rift valleys here:
brainly.com/question/21029520
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The 2010 Census enumerated 308.7 million people in the United States, a 9.7 percent increase from 281.4 million in Census 2000. Of the total population in 2010, 300.8 million lived in 116.7 million households for an average of 2.58 people per household.
