Write prototypes and implementations for $3$ non$-$member functions named R$1,$ R$2,$ and R$3$ that

each accept an angle in units of radians and return objects of the Matrix class corresponding to the

following rotation matrices that rotate clockwise about the $1,2,3$ or x$,$y$,$z axes:

$1()=[$

$100$

$0$ cos$$ sin$$

$0$sin$$ cos$$

$]$

$2()=[$

cos$0$sin$$

$010$

sin$0$ cos$$

$]$

$3()=[$

cos$$ sin$0$

$$sin$$ cos$0$

$001$

$]$

$($Note that you may see different versions of these rotation matrices with the other sin element

being negative, this is due to rotation in a different direction$)$

$4.$ To perform arithmetic operations on matrices, you can use non$-$member functions, member

functions, or overloaded operators $($which are a special type of member function where the function

name is the operator and the syntax for calling the function uses the operator.$)$ Three non$-$member

functions have the following prototypes:Matrix Multiply$($const Matrix& A$,$ const Matrix& B$)$;

Matrix Multiply$($const Matrix& A$,$ double k$)$;

Matrix Add$($const Matrix& A$,$ Matrix& B$)$;

The second multiply function is an overload because multiply is different when you are

multiplying a Matrix by a scalar $($different in both linear algebra and in C$++,$ we need to tell the

compiler how to do this$)$

a$.$ Write prototypes for the corresponding member functions. These member functions

should not change the matrix object, but should ask the Matrix object to determine and

return the results of:

i$.$ multiplying itself by another matrix,

ii$.$ multiplying itself by a scalar $($a double$)$

iii. adding itself to another matrix.

b$.$ Write prototypes of member functions that overload the $*$ and $+$ operators for the same

three cases listed above