Please make changes to the following java code following the instruciton of tasks posted with this question. Please make use of the resources, the code should not be too complicated. The code is correct if it runs with the test code below correctly. Thank you

The code to be edited:

class MathVector $\{$

final int dim;

final double$[]$ values;

public MathVector$($int N$)\{$

dim $=$ N;

values $=$ new double$[$N$]$;

$\}$

public MathVector$($double$[]$ arr$)\{$

dim $=$ arr.length;

values $=$ new double$[$arr$.$length$]$;

$\}$

public MathVector$($MathVector v$)\{$

dim $=0$;

values $=$ null;

$\}$

public static MathVector vec$2$DfromPolar$($double r$,$ double theta$)\{$

return new MathVector$(0)$;

$\}$

public static MathVector vec$3$DfromPolar$($double r$,$ double theta, double phi$)\{$

return new MathVector$(0)$;

$\}$

public int getDimension$()\{$ return $0$; $\}$

public double getValue$($int idx$)\{$ return $0$; $\}$

public void setValue$($int idx, double val$)\{\}$

public double dotWith$($MathVector other$)\{$ return $0$; $\}$

public double getMagnitude$()\{$ return $0$; $\}$

public void scaleBy$($double scalar$)\{\}$

public static MathVector multiply$($double scalar, MathVector v$)\{$

return new MathVector$(0)$;

$\}$

public void shiftBy$($MathVector other$)\{\}$

public static MathVector add$($MathVector v$1,$ MathVector v$2)\{$

return new MathVector$(0)$;

$\}$

public static MathVector add$($MathVector$...$ vs$)\{$

return new MathVector$(0)$;

$\}$

public boolean equals$($MathVector other$)\{$ return false; $\}$

public String toString$()\{$ return $""$; $\}$

public void print$()\{\}$

$\}$

The code to be tested:

class HW$2\_$Tester $\{$

public static void main$($String$[]$ args$)\{$

MathVector v$1=$ new MathVector$(1)$;

MathVector v$2=$ new MathVector$(1\mathrm{.}0,2\mathrm{.}0)$;

MathVector v$3=$ new MathVector$($v$2)$;

System.out.println$($v$1.$getDimension$()+""+$ v$2.$getDimension$())$; $//12$

System.out.println$($v$1.$getValue$(1))$; $//0\mathrm{.}0$

System.out.print$(\text{'}$

$\text{'})$;

v$3.$setValue$(2,3\mathrm{.}0)$;

System.out.println$($v$1.$toString$())$; $//[0\mathrm{.}0]$

System.out.println$($v$2)$; $//[1\mathrm{.}0,2\mathrm{.}0]$

v$3.$print$()$; $//[1\mathrm{.}0,3\mathrm{.}0]$

System.out.print$(\text{'}$

$\text{'})$;

MathVector.vec$2$DfromPolar$(2,$ Math.PI $/3).$print$()$;

$//$ close to $[1\mathrm{.}0,$ Math.sqrt$(3\mathrm{.}0)]$

MathVector.vec$3$DfromPolar$(4,$ Math.PI $/6,$ Math.PI $/3).$print$()$;

$//$ close to $[1\mathrm{.}0,$ Math.sqrt$(3\mathrm{.}0),2*$ Math.sqrt$(3)]$

System.out.print$(\text{'}$

$\text{'})$;

MathVector v $=$ new MathVector$(1,2,0,0)$;

MathVector w $=$ new MathVector$(0,0,3,4)$;

final MathVector e$1=$ new MathVector$(1,0,0,0)$;

final MathVector e$2=$ new MathVector$(0,1,0,0)$;

final MathVector e$3=$ new MathVector$(0,0,1,0)$;

final MathVector e$4=$ new MathVector$(0,0,0,1)$;

System.out.println$($v$.$dotWith$($e$1))$; $//1\mathrm{.}0$

System.out.println$($v$.$dotWith$($e$2))$; $//2\mathrm{.}0$

System.out.println$($w$.$dotWith$($w$))$; $//25\mathrm{.}0$

System.out.println$($w$.$getMagnitude$())$; $//5\mathrm{.}0$

System.out.print$(\text{'}$

$\text{'})$;

System.out.println$($MathVector$.$multiply$(2,$ w$))$; $//[0\mathrm{.}0,0\mathrm{.}0,6\mathrm{.}0,8\mathrm{.}0]$

w$.$print$()$; $//$ w unchanged by line before $//[0\mathrm{.}0,0\mathrm{.}0,3\mathrm{.}0,4\mathrm{.}0]$

w$.$scaleBy$(2)$;

w$.$print$()$; $//$ w changed by line before $//[0\mathrm{.}0,0\mathrm{.}0,6\mathrm{.}0,8\mathrm{.}0]$

System.out.print$(\text{'}$

$\text{'})$;

System.out.println$($MathVector$.$add$($v$,$ w$))$; $//[1\mathrm{.}0,2\mathrm{.}0,6\mathrm{.}0,8\mathrm{.}0]$

v$.$print$()$; $//$ v unchanged by line before $//[1\mathrm{.}0,2\mathrm{.}0,0\mathrm{.}0,0\mathrm{.}0]$

w$.$print$()$; $//$ w unchanged by line before $//[0\mathrm{.}0,0\mathrm{.}0,6\mathrm{.}0,8\mathrm{.}0]$

System.out.print$(\text{'}$

$\text{'})$;

v$.$shiftBy$($w$)$;

v$.$print$()$; $//$ v changed by line before $//[1\mathrm{.}0,2\mathrm{.}0,6\mathrm{.}0,8\mathrm{.}0]$

w$.$print$()$; $//$ w unchanged by line before $//[0\mathrm{.}0,0\mathrm{.}0,6\mathrm{.}0,8\mathrm{.}0]$

System.out.print$(\text{'}$

$\text{'})$;

MathVector linearCombination $=$ MathVector.add$($

MathVector.multiply$(8,$ e$1),$ MathVector.multiply$(7,$ e$2),$

MathVector.multiply$(6,$ e$3),$ MathVector.multiply$(5,$ e$4)$

$)$;

linearCombination.print$()$; $//[8\mathrm{.}0,7\mathrm{.}0,6\mathrm{.}0,5\mathrm{.}0]$

System.out.print$(\text{'}$

$\text{'})$;

System.out.println$(!$e$1.$equals$($e$2))$; $//$ true

System.out.println$(!$e$2.$equals$($e$3))$; $//$ true

System.out.println$(!$e$3.$equals$($e$4))$; $//$ true

System.out.println$(!($new MathVector$(4)).$equals$($new MathVector$(5)))$; $//$ true

System.out.println$($v$.$equals$($v$))$; $//$ true

System.out.println$($w$.$equals$($w$))$; $//$ true

System.out.println$($w$.$equals$($new MathVectWe have