Answer:
p ∈ IR - {6}
Step-by-step explanation:
The set of all linear combination of two vectors ''u'' and ''v'' that belong to R2
is all R2 ⇔
And also u and v must be linearly independent.
In order to achieve the final condition, we can make a matrix that belongs to 
using the vectors ''u'' and ''v'' to form its columns, and next calculate the determinant. Finally, we will need that this determinant must be different to zero.
Let's make the matrix :
![A=\left[\begin{array}{cc}3&1&p&2\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%261%26p%262%5Cend%7Barray%7D%5Cright%5D)
We used the first vector ''u'' as the first column of the matrix A
We used the second vector ''v'' as the second column of the matrix A
The determinant of the matrix ''A'' is
We need this determinant to be different to zero
The only restriction in order to the set of all linear combination of ''u'' and ''v'' to be R2 is that
We can write : p ∈ IR - {6}
Notice that is 
⇒
If we write 
, the vectors ''u'' and ''v'' wouldn't be linearly independent and therefore the set of all linear combination of ''u'' and ''b'' wouldn't be R2.
To find a volume of a cylinder we use the following formula:
Plug in the values:
Take the square:
Multiply the numbers:
Answer:
six
Step-by-step explanation:
1,000,000
Answer:
120 people/sq. mile
Step-by-step explanation:
Population Density is the concept of how "crowdy" a place is. The more the population density, the more crowded that place is.
The population density is found by dividing the "number of people" by the "land area" (in sq mile or sq km).
Here, it is given there are 600 million people, so
Number of People = 600,000,000
And, the land area is given as 5 million square miles, so
Land Area = 5,000,000 sq. miles
Hence,
Population Density = 600,000,000/5,000,000 = 120 people/sq. mile
Answer:
1114$
Step-by-step explanation:
