Answer:
a) False
b) False
c) True
d) False
e) False
Step-by-step explanation:
a. A single vector by itself is linearly dependent. False
If v = 0 then the only scalar c such that cv = 0 is c = 0. Hence, 1vl is linearly independent. A set consisting of a single vector v is linearly dependent if and only if v = 0. Therefore, only a single zero vector is linearly dependent, while any set consisting of a single nonzero vector is linearly independent.
b. If H= Span{b1,....bp}, then {b1,...bp} is a basis for H. False
A sets forms a basis for vector space, only if it is linearly independent and spans the space. The fact that it is a spanning set alone is not sufficient enough to form a basis.
c. The columns of an invertible n × n matrix form a basis for Rⁿ. True
If a matrix is invertible, then its columns are linearly independent and every row has a pivot element. The columns, can therefore, form a basis for Rⁿ.
d. In some cases, the linear dependence relations among the columns of a matrix can be affected by certain elementary row operations on the matrix. False
Row operations can not affect linear dependence among the columns of a matrix.
e. A basis is a spanning set that is as large as possible. False
A basis is not a large spanning set. A basis is the smallest spanning set.
The radius of your cone is half of 18 units = 9 units.
The volume of any cone is <span><span>V = (1/3) · (pi) · (radius)² · (height) </span>
</span>
-- Take that formula for the volume of any cone.
-- Write '8' in place of 'height'.
-- Write '9' in place of 'radius'.
-- Write '3.142' in place of 'pi'.
-- Complete the arithmetic.
-- Bada-bing, you've got the volume.
Answer:
option D is the right answer
Answer:
I assume not
Step-by-step explanation:
Answer:
The confidence level of the study is 99.9%
The confidence level is 99.9% of the margin error is 8%
Step-by-step explanation:
<u>Explanation</u>:-
Candy has observed 250 sports cars
The sample size 'n' = 250
Sample proportion 'p' = 15% = 0.15
The margin of error = 8% = 0.08
<em>The margin of error is determined by </em><em> = </em>
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<u>Conclusion</u>:-
The z- score of 99.9% level of significance = 3.54 for two tailed test
<em>Hence the confidence level is 99.9% of the margin error is 8%.</em>
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