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.
Ok so she wants but 5 crates of apples. And each crate cost 12.50 so you would multi 12.50 times 5, which is 62.05. She so wants to buy one crate of pears. One crate of pairs is 18.75. Since she is only buying one you don't need to multiply it but anything. But now you have to figure out the cost of the apples and pears together. So just add 62.05 and 18.75 together which is 80.80
Total gasoline = 10 gallons
Gasoline left after 100 miles = 5 gallons
Gasoline used in 100 miles
= Total gasoline - Gasoline left after 100 miles
= 10 gallons - 5 gallons
= 5 gallons
Gasoline used in 1 mile
= Gasoline used in 100 miles/100
= 5 gallons/100
= 0.05 gallons
5(2)^2-2(7) = 6
6(7+2)/2 = 27
Therefor the correct answer is the < symbol.
I hope this helps! :)
