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grandymaker [24]
3 years ago
15

What are the coordinates of (3 comma space 8 )relative to the basis open curly brackets space (1 comma space 1 )comma space (0 c

omma space 1 )space close curly brackets
Computers and Technology
1 answer:
Snowcat [4.5K]3 years ago
5 0

Answer:

(3,5)

Explanation:

Given the basis β={(1,1),(0,1)} and x=(3,8), I am to find the corresponding coordinate vector [x]β. I claim that the coordinate vectors entries x_{1} and x_{2} meet the following criterion:

x_{1} (1,1) +x_{2} (0,1)=(3,8)

Placing this in matrix form

\left(\begin{array}{cc}1 & 0\\ 1 & 1 \end{array} \right)\left(\begin{array}{c}x_{1} \\ x_{2}\end{array} \right)

x_{1} +0x_{2} =3

x_{1} =3

Also,

1x_{1} +1x_{2} =8

3 + 1x_{2} =8

x_{2} =8-3=5

The coordinate matrix therefore is given as (3,5)

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In Java: Write a class called Shelf that contains instance data that repre-sents the length, breadth, and capacity of the shelf.
disa [49]

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Explanation:

Hello, the solution is the following:

in a file named Shelf.java :

public class Shelf{

   int length;

   int breadth;

   int capacity;

   boolean occupied;

   Shelf(int length,int breadth, int capacity){

       this.length = length;

       this.breadth = breadth;

       this.capacity = capacity;

       this.occupied = false;

   }

   

   //set methods

   public void setLength(int length){

       this.length = length;

   }

   public void setBreadth(int breadth){

       this.breadth = breadth;

   }

   public void setCapacity(int capacity){

       this.capacity = capacity;

   }

   public void setOccupied(boolean occupied){

       this.occupied = occupied;

   }

   

   //get methods

   public int getLength(){

       return this.length;

   }

   public int getBreadth(){

       return this.breadth;

   }

   public int getCapacity(){

       return this.capacity;

   }

   public boolean getOccupied(){

       return this.occupied;

   }

   

   //tostring method

   

   public String toString(){//overriding the toString() method  

 return "Shelf: \n"+" length: "+Integer.toString(this.length)+" breadth: "+Integer.toString(this.breadth)+" capacity: "+Integer.toString(this.capacity)+" occupied: "+Boolean.toString(this.occupied);

}  

}

in another file named ShelfCheck.java

public class ShelfCheck {

 public static void main(String[] args) {

   Shelf s1=new Shelf(100,150,300);

   Shelf s2=new Shelf(200,200,234);  

   Shelf s3=new Shelf(300,222,543);  

   Shelf s4=new Shelf(400,434,654);

   System.out.println(s1);

   System.out.println(s2);

   System.out.println(s3);

   System.out.println(s4);

   s4.setLength(5);

   System.out.println(s4);

   s2.setBreadth(2);

   System.out.println(s2);

   s3.setCapacity(1);

   System.out.println(s3);

   s1.setOccupied(true);

   System.out.println(s1);

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}

OUTPUT:

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length: 100 breadth: 150 capacity: 300 occupied: false

Shelf:

length: 200 breadth: 200 capacity: 234 occupied: false

Shelf:

length: 300 breadth: 222 capacity: 543 occupied: false

Shelf:

length: 400 breadth: 434 capacity: 654 occupied: false

Shelf:

length: 5 breadth: 434 capacity: 654 occupied: false

Shelf:

length: 200 breadth: 2 capacity: 234 occupied: false

Shelf:

length: 300 breadth: 222 capacity: 1 occupied: false

Shelf:

length: 100 breadth: 150 capacity: 300 occupied: true

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3 years ago
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