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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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Import java.awt.GridLayout;
Vikki [24]

Answer:

public class ConversionCalculator extends JFrame {

  private JLabel inch_Label, meter_Label, cm_Label, yard_Label;

  private JButton clear, calculate, exit;

  private JTextField inch_tf, cm_tf, meters_tf, yards_tf;

 

  public ConversionCalculator()

  {

     

      exitButtonHandler exitB;

      clearButtonHandler clearB;

      calcButtonHandler calcB;

     

      setTitle("Conversion Calculator");

      setSize(600,200);

      setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

     

      //The first layout we use will be 1 row with three columns

      setLayout(new GridLayout(1,3));

     

      //initialize all the components

      inch_Label = new JLabel("Inches");

      meter_Label = new JLabel("Meters");

      cm_Label = new JLabel("Centimeters");

      yard_Label = new JLabel("Yards");

      clear = new JButton("Clear");

      calculate = new JButton("Calculate");

      exit = new JButton("Exit");

      inch_tf = new JTextField("0.00");

      cm_tf = new JTextField("0.00");

      meters_tf = new JTextField("0.00");

      yards_tf = new JTextField("0.00");

 

      JPanel panel1 = new JPanel();

      panel1.setLayout(new GridLayout(2,2));

      JPanel panel2 = new JPanel();

      panel2.setLayout(new GridLayout(2,2));

      JPanel panel3 = new JPanel();

      panel3.setLayout(new GridLayout(3,1));

      panel1.add(cm_Label);

      panel1.add(cm_tf);

      panel1.add(meter_Label);

      panel1.add(meters_tf);

     

      panel2.add(inch_Label);

      panel2.add(inch_tf);

      panel2.add(yard_Label);

      panel2.add(yards_tf);

     

      panel3.add(clear);

      panel3.add(calculate);

      panel3.add(exit);

     

      add(panel1);

      add(panel2);

      add(panel3);

     

     

      exitB = new exitButtonHandler();

      exit.addActionListener(exitB);

     

      clearB = new clearButtonHandler();

      clear.addActionListener(clearB);

     

      calcB = new calcButtonHandler();

      calculate.addActionListener(calcB);

     

      setVisible(true);

  }

 

  //public static void main(String[] args)

     // {

       // new ConversionCalculator();

      //}

 

  private class exitButtonHandler implements ActionListener

  {

      public void actionPerformed(ActionEvent e)

      {

          //exits program

          System.exit(0);

      }

  }

 

  private class clearButtonHandler implements ActionListener

  {

      public void actionPerformed(ActionEvent e)

      {

          //clear button sets all text fields to 0

          inch_tf.setText("0.00");

          meters_tf.setText("0.00");

          yards_tf.setText("0.00");

          cm_tf.setText("0.00");

      }

  }

 

  private class calcButtonHandler implements ActionListener

  {

      public void actionPerformed(ActionEvent e)

      {

          double inches, yards, meters, cms;

          DecimalFormat df = new DecimalFormat("0.00");

         

          //parse strings in textbox into doubles

          inches = Double.parseDouble(inch_tf.getText());

          yards = Double.parseDouble(yards_tf.getText());

          meters = Double.parseDouble(meters_tf.getText());

          cms = Double.parseDouble(cm_tf.getText());

         

          //we check which value has been tampered with and base our conversion off this

          //because of this it is important that the user clears, or else it will do inch conversion

          if(inches != 0.00)

          {

              cms = inches * 2.54;

              meters = cms / 100;

              yards = inches / 36;

             

              cm_tf.setText(df.format(cms));

              meters_tf.setText(df.format(meters));

              yards_tf.setText(df.format(yards));

             

          }

          else if(yards != 0.00)

          {

              inches = yards / 36;

              cms = inches * 2.54;

              meters = cms / 100;

             

              cm_tf.setText(df.format(cms));

              meters_tf.setText(df.format(meters));

              inch_tf.setText(df.format(inches));

          }

          else if(meters != 0.00)

          {

              cms = meters * 100;

              inches = cms / 2.54;

              yards = inches / 36;

             

              cm_tf.setText(df.format(cms));

              inch_tf.setText(df.format(inches));

              yards_tf.setText(df.format(yards));

          }

          else if(cms != 0.00)

          {

              inches = cms / 2.54;

              yards = inches / 36;

              meters = cms / 100;

             

              meters_tf.setText(df.format(meters));

              inch_tf.setText(df.format(inches));

              yards_tf.setText(df.format(yards));

          }

      }

  }

}

Explanation:

  • Inside the action performed method, pass the strings in text box.
  • check if the value has been modified then do the relevant conversions inside the conditional statement.
  • When the user clears, it will not do to the inch conversion.
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