By definition, if 
is the least upper bound of the set 
, it means two thing:
In other words, the least upper bound of a set is greater than or equal to every single element of the set, but it is "close enough" to the elements of the set, because you guaranteed to find elements in the set between 
and 
For example, pick 
. Obvisouly, the least upper bound is 
. In fact, every number in 
is smaller than 10, but as soon as you take away something from 10, say 0.01, you get 9.99, and there are elements in greater than 9.99, say 9.9999.
So, the claim is basically proven by definition: if 
, let 
. By definition, there exists 
.
Percent means parts out of 100
30%=30/100=3/10
3/10 out of 720000 means 3/10 times 720,000=2160000/10=216,000
the answer is 216,000
Answer:
No is not the solution to that system
Step-by-step explanation:
Answer:
The middle answer
Step-by-step explanation:
Because if you did 4 x 10 - 10 that would give you 30
but if you did
3 x (44 - 3 x (6 + 6)) that would give you 1476 so the middle answer is correct
Answer : Dimension of column A is also be 4 whereas the two vector basis lie in R⁴.
The smallest possible dimension of Nul A would be zero.
Step-by-step explanation:
Since we have given that
A is matrix of 4 x 9 .
so, Number of rows = 4
Number of columns = 9
Nul A = 5
It means that Rank of A would be 9 - 5 =4
So, rank A = 4
Thus, dimension of column A is also be 4 whereas the four vector basis lie in R⁴.
So, dim Col A = 4
If A is 7 x 3 matrix.
So, we know that
rank A + dim (null A) = 3
so, it is possible to have rank A = 3 so the dim col A should be 3
Then the smallest possible dimension of Nul A would be zero.
