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.
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.
Answer:
#include <iostream>
using namespace std;
class Digits
{
public:
int num;
int read() //method to read num from user
{
cout<<"Enter number(>0)\n";
cin>>num;
return num;
}
int digit_count(int num) //method to count number of digits of num
{
int count=0;
while(num>0) //loop till num>0
{
num/=10;
count++; //counter which counts number of digits
}
return count;
}
int countDigits(int num) //method to return remainder
{
int c=digit_count(num); //calls method inside method
return num%c;
}
};
int main()
{
Digits d; //object of class Digits is created
int number=d.read(); //num is read from user
cout<<"\nRemainder is : "<<d.countDigits(number); //used to find remainder
return 0;
}
Output :
Enter number(>0)
343
Remainder is : 1
Explanation:
As program is missing to find errors , a logically write program is written to find the remainder when a number is divided by its number of digits. A class Digits is constructed which has public variable num and methods read(), digit_count(), countDigits().
- read() - This method reads value of num from the user and return num.
- digit_count() - This method takes a integer as parameter and counts the number of digits of a number passed as argument. while loop is used to increement the counter until num<0. This returns the value of count.
- countDigits() - This method takes a integer as a parameter and returns remainder when the argument is divided by number of digits of argument. Number of digits is calculated by using method digit_count().
At last in main method , object of Digits class is created and its methods are used to find the output.
Answer:
The Internet began as a US Department of Defense network named Advanced Research Project Agency Network (ARPANET) funded by the Advanced Research Project Agency (ARPA, later DARPA). In the 1970s, universities and other educational institutions began sharing this technology. The network grew as more and more users began sharing information.However, the information being shared on this network was very limited because of its government ties. The ARPANET was decommissioned in 1990. This move was followed by the commercialization of the Internet, which allowed it to carry business and personal traffic.
Explanation:
Answer:
Follows are the matching to this question:
Explanation:
Column A Column B
1 c
2 d
3 b
4 a
Description of the matching:
- In 1(Acid) the correct choice is (c) because the acid (HCl) dissociates to both the H+ ion and the Cl- ion as a solution.
- In 2(Alkaline ) the correct choice is (d) because alkaline NaOH is a solution that differentiates between the ions ( OH-) and Na+.
- In 3(pH ) the correct choice is (b) because for an A compound of less than 7 is an acid and an alkaline pH compound of more than 7. For neutral compounds, a pH of 7 is applicable.
- In 4(Ion) the correct choice is (a) because Na+ ion is loaded positive, and Cl-ion is loaded negatively.
Answer:
The program in C++ is as follows:
#include <iostream>
using namespace std;
int main(){
int qty;
float discount = 0;
cout<<"Quantity: ";
cin>>qty;
int cost = qty * 100;
{ 
; }
cout<<"Cost: "<<cost - discount;
return 0;
}
Explanation:
This declares the quantity as integer
int qty;
This declares and initializes discount to 0
float discount = 0;
This prompts the user for quantity
cout<<"Quantity: ";
This gets input for quantity
cin>>qty;
This calculates the cost
int cost = qty * 100;
If cost is above 1000, a discount of 10% is calculated
{ ; }
This prints the cost
cout<<"Cost: "<<cost - discount;
