Needs MATLAB A Vandermonde matrix is an n times n matrix formed from a vector w

Question

Needs MATLAB

A Vandermonde matrix is an n times n matrix formed from a vector w vector = (w_0, w_1, w_2, ..., w_n - 1) as follows: V(w vetcor) = (w^n - 1_0 w^n - 1_0 w^2_0 w_0 1 w^n - 1_1 w^n - 2_1 w^2_1 w_1 1 w^n - 1_2 w^n - 2_2 w^2_2 w_2 1 w^n - 1_n - 1 w^n - 2_n - 2 w^2_n - 1 w_n - 1 1). You may generate Vandermonde matrices using the MATLAB command vander. which takes the vector w vector as its single parameter. (a) Consider the Vandermonde matrix generated with w vector= [10.0: 0.1: 11.0]. Solve the system V(w vector)x vector = b vector where b vector = [1; 9; 1;9; 1;9; 1; 9; 1;9; 1]^T using LU decomposition and Forward/Backward solver. Plug your answer back into the system and compute the result. What do you observe? Provide the result you computed. (You can use your code from Question 3, or Matlab's built-in linear solver. You can check (not required) that PALU does in this case not lead to more accurate results than LU.) (b) Compute the condition number of the matrix V(w vector) and use this to explain the observed discrepancy. (You may calculate the condition number of a matrix A using the cond command. This command returns an explicit value of the condition number for the provided matrix.)

Explanation / Answer

open class CarPanel develops JPanel {
private roast forwardKey = 'w';
private boolean reachedTarget = false;
private Color shading = Color.blue;
private int x= 10;
private int y= 10;
private int panelWidth;
private int panelHeight;
/default Constructor
open CarPanel(){
}
/over-burden Constructor
open CarPanel(char scratch, Color color){
this.forwardKey=key;
this.color = shading;
}
ensured void paintComponent(Graphics g){
super.paintComponent(g);
panelWidth= getWidth();
panelHeight= getHeight();
/draw a Car
g.setColor(color);
/polygon focuses
int t_x[]= {x+10,x+20,x+30,x+40};
int t_y[]= {y+10,y,y,y+10};
g.fillPolygon(t_x,t_y,t_x.length);
g.fillRect(x, y+10, 50, 10);
g.fillArc(x+10, y+20, 10, 10, 0, 360);
g.fillArc(x+30, y+20, 10, 10, 0, 360);
}
@Override
open Dimension getPreferredSize() {
return new Dimension(750,100);
}
open void moveCar(){
if(this.x < panelWidth){
this.x+=10;
repaint();
}
}
}

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