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.
Answer:
2 
Step-by-step explanation:
The question state that; the sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2. Find the number.
First, we need to interpret and represent this statement mathematically
Let n be the number.
The sum means 'addition'
1/6 of that number is 1/6 of n = 1/6 × n = 
2 1/2 of that number is 2 1/2 of n = 2 1/2 × n = 5/2 × n = 
So the question says that, when we add; , and 7 all together, the value is 12 1/2
That is;
+ + 7 = 12 1/2
+ + 7 = 
( changing 12 1/2 to improper fraction will give )
So we can now go ahead and solve for n
+ + 7 =
subtract 7 from both-side of the equation
+ = - 7
= 
= 
can be reduced to give us 
=
Cross multiply
8n × 2 = 11× 3
16n = 33
Divide both-side of the equation by 16
= 
(On the left-hand side of the equation, 16 will cancel-out 16 leaving us with just, while on the right-hand side of the equation 33 will be divided by 16)
n = = 
Therefore the number is
Answer:
Step-by-step explanation:
43/60
How many three-fourths are in 2? 2 complete sets of three-fourths can be made and 2 of the 3 pieces need to make \frac34 are left over, so we have another \frac23 of a three-fourths. and we can see that there are 2 wholes with 4 fourths in each whole, so there are 2\times 4 fourths in 2.
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