In linear algebra, the rank of a matrix
A
A is the dimension of the vector space generated (or spanned) by its columns.[1] This corresponds to the maximal number of linearly independent columns of
A
A. This, in turn, is identical to the dimension of the vector space spanned by its rows.[2] Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by
A
A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.
The rank is commonly denoted by
rank
(
A
)
{\displaystyle \operatorname {rank} (A)} or
rk
(
A
)
{\displaystyle \operatorname {rk} (A)}; sometimes the parentheses are not written, as in
rank
A
{\displaystyle \operatorname {rank} A}.
Answer:
The function is increasing on the interval [-2,1]
Step-by-step explanation:
Answer:
0.81
Step-by-step explanation:
For this problem, we are going to use the <em>law of sines</em>, which states:
In this case, we have an angle and two sides, and we are trying to look for the third side. First, we have to find the angle which corresponds with the second side, 
. Then, we can find the third side. Using the law of sines, we can find:
We can use this to solve for :
Now, we can find 
:
Using this, we can find 
:
c is approximately 17.5.
