Answer:
is linearly dependent set.
Step-by-step explanation:
Given: 
is a linearly dependent set in set of real numbers R
To show: the set is linearly dependent.
Solution:
If 
is a set of linearly dependent vectors then there exists atleast one 
such that 
Consider 
A linear transformation T: U→V satisfies the following properties:
1. 
2. 
Here, 
∈ U
As T is a linear transformation,
As is a linearly dependent set,
for some 
So, for some
Therefore, set is linearly dependent.
Answer:
16 and 48
Step-by-step explanation:
let the 2 integers be x and 3x ← ratio 1 : 3
Then
3x - x = 32 ← difference between the integers
2x = 32 ( divide both sides by 2 )
x = 16
and 3x = 3 × 16 = 48
Since magnitude of difference is 32
We can also express the difference as
x - 3x = 32
- 2x = 32 ( divide both sides by - 2 )
x = - 16
and 3x = 3 × - 16 = - 48
The 2 integers are 16 and 48 or - 16 and - 48
Answer: OPTION D.
Step-by-step explanation:
The formula for calculate the circumference of a circle is:
Where <em>r</em> is the radius.
The formula for calculate the area of a circle is:
Where <em>r</em> is the radius.
Solve for <em>r</em> from to calculate it:
Subsitute the radius into . Then:
Answer:
Step-by-step explanation:
-60
Step-by-step explanation:
Increase in population is given by positive sign
Change in population in 5 years = -300
Decrease in population is represented by negative sign
Change in population in 1 year = -300\5
= -60
Town's population faces a decrease of 60 residents each year.
