Solution:
A function is always a relation but a relation is not always a fucntion.
For example
we can make a realtion of student roll number and their marks obtained in mathematics.
So we can have pairs like (a,b), (c,d)..etc.
Its a realtion but it may not be function. Because function follows that for same input there should not be diffrent output, aslo there could be many inputs to one output in the case of constant function . But this doesn't holds a necessary condition in case of relation.
Because two diffrent students with two diffrent Roll number may have same marks.
Hence the foolowing options holds True in case of a function.
A) many inputs to many outputs or one input to one output.
D) one input to one output or many inputs to one output.
Answer:
≈ -5.1857
≈ -5.4857
≈ 3.7262
Step-by-step explanation:
Rewrite the equation system as:
Now, write the system in its augmented matrix form:
![\left[\begin{array}{cccc}6&8&0&-75\\-3&6&6&5\\2&-9&0&39\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D6%268%260%26-75%5C%5C-3%266%266%265%5C%5C2%26-9%260%2639%5Cend%7Barray%7D%5Cright%5D)
applying row reduction process to its associated augmented matrix:
Swap R1 and R3, and then Swap R1 and R2:
![\left[\begin{array}{cccc}-3&6&6&5\\2&-9&0&39\\6&8&0&-75\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-3%266%266%265%5C%5C2%26-9%260%2639%5C%5C6%268%260%26-75%5Cend%7Barray%7D%5Cright%5D)
R3+2R1
![\left[\begin{array}{cccc}-3&6&6&5\\2&-9&0&39\\0&20&12&-65\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-3%266%266%265%5C%5C2%26-9%260%2639%5C%5C0%2620%2612%26-65%5Cend%7Barray%7D%5Cright%5D)
3R2+2R1
![\left[\begin{array}{cccc}-3&6&6&5\\0&-15&12&127\\0&20&12&-65\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-3%266%266%265%5C%5C0%26-15%2612%26127%5C%5C0%2620%2612%26-65%5Cend%7Barray%7D%5Cright%5D)
15R3+20R2
![\left[\begin{array}{cccc}-3&6&6&5\\0&-15&12&127\\0&0&420&1565\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-3%266%266%265%5C%5C0%26-15%2612%26127%5C%5C0%260%26420%261565%5Cend%7Barray%7D%5Cright%5D)
Now we have a simplified system:
From (3):
(4)
Replacing (4) in (2)
(5)
Finally replacing (5) and (4) in (1)
<span>π </span>* 6 = 18.8495559215 / 4 = 4.71238898038
