Answer:
The statements which are true are;
- A user-defined data type can include other user-defined data types
- A user-defined data type is defined using a class
- A user-defined data type can include a list
Explanation:
A user-defined data type (UDT) is a datatype that is defined and derived by the use of the datatypes which preexist including existing user-defined datatypes and the built-in datatypes
It is therefore true that a user-defined data type can include other user-defined data types
A class is a user-defined data type that contains both its member data and member functions, that can be used when an instance of the class is first created
Therefore, a user-defined data type is defined using a class
In a user-defined data type, a variable has actual data within it which can include an array or list
Therefore a user-defined data type can include a list.
Answer:
The Rouché-Capelli Theorem. This theorem establishes a connection between how a linear system behaves and the ranks of its coefficient matrix (A) and its counterpart the augmented matrix.
![rank(A)=rank\left ( \left [ A|B \right ] \right )\:and\:n=rank(A)](https://tex.z-dn.net/?f=rank%28A%29%3Drank%5Cleft%20%28%20%5Cleft%20%5B%20A%7CB%20%5Cright%20%5D%20%5Cright%20%29%5C%3Aand%5C%3An%3Drank%28A%29)
Then satisfying this theorem the system is consistent and has one single solution.
Explanation:
1) To answer that, you should have to know The Rouché-Capelli Theorem. This theorem establishes a connection between how a linear system behaves and the ranks of its coefficient matrix (A) and its counterpart the augmented matrix.
![rank(A)=rank\left ( \left [ A|B \right ] \right )\:and\:n=rank(A)](https://tex.z-dn.net/?f=rank%28A%29%3Drank%5Cleft%20%28%20%5Cleft%20%5B%20A%7CB%20%5Cright%20%5D%20%5Cright%20%29%5C%3Aand%5C%3An%3Drank%28A%29)

Then the system is consistent and has a unique solution.
<em>E.g.</em>

2) Writing it as Linear system


3) The Rank (A) is 3 found through Gauss elimination


4) The rank of (A|B) is also equal to 3, found through Gauss elimination:
So this linear system is consistent and has a unique solution.