Question A2: Defining Vectors (9 points) Define class Vector for n-dimensional vectors as follows: Vector( l) : Creates a new vector with dimension...

Define class Vector for n-dimensional vectors as follows:

• Vector(l): Creates a new vector with dimension len(l) from list l of numbers; raises TypeError if l is not a list or not all of its elements are of type int or float.
• v.dim(): Returns the dimension (length) of the vector.
• v. __getitem__(i): Returns the i-th component of the vector, where components are indexed starting from 1; raises IndexError if i is less than 1 or greater than the dimension of the vector.
• v. __setitem__(i, x): Sets the i-th component of vector v to x, where components are indexed starting from 1; raises IndexError if i is less than 1 or greater than the dimension of the vector.
• v.__repr__(): Returns the canonical string representation of the vector, see the example below.
• v. __add__(other): Returns a new vector that is the component-wise sum of v and other; raises ValueError if other is not of type Vector or if other is of a different dimension.
• v. __sub__(other): Returns a new vector that is the component-wise substraction of v and other; raises ValueError if other is not of type Vector or if other is of a different dimension.
• v.__mul__(other): If other is of type int or float, returns a new vector resulting from the scalar multiplication of v with other, , i.e. with each component of v multiplied by scalar. If other is of type Vector, returns the dot product of v and other, which is the sum of the products of the corresponding components; raises ValueError if other is of different dimension in this case. If the type of other is none of Vector, int, float, raises AssertionError. 
• v.__rmul__(other): Defined exactly like v.__mul__(other)
• v.__equal__(self, other): Returns True if the values of the vector equals the values of other and are in the same order.