The following class named Matrix has a template given to you. The init$()$ method takes $2$ parameters. The parameter name is a string, and the parameter data is a nested list representing a Matrix. $($Each element in data is a list of elements for that row$).$

For example $[[1,2],[3,4]]$ represents

$12$

$34$

Modify the class according to the following specifications

Write a method named Average. Matrix.Average$()$ should return the average of all values in the matrix as a float. Assume the average of an empty matrix is $0.$

Overload the subtraction operator so that you can subtract two matrices from each other. Subtracting $2$ Matrices should result in a new matrix. If the matrices are the same side then the result is a new matrix. The new matrix will have the 'Matrix$1.$name $-$ Matrix$2.$name'. The data for the matrix should be element by element subtraction of the second matrix from the first. If the matrices are not the same size, then the method should return the string 'error'.

Overload the addition operator so that if the matrix is added to a value $($integer or float$),$ all values in the matrix increase by that value

Examples

Example $1$ Code:

a $=$ Matrix$(\text{'}$a$\text{'},[[9,8],[7,6]])$

print$($a$)$ # this should work with the template

Example $1$ Output:

a$=$

$98$

$76$

Example $2$ Code:

a $=$ Matrix$(\text{'}$a$\text{'},[[9,8],[7,6]])$

avg $=$ a$.$Average$()$

print$($avg$)$ # this should work with the template

Example $2$ Output:

$7\mathrm{.}5$

Example $3$ Code:

a $=$ Matrix$(\text{'}$a$\text{'},[[9,8],[7,6]])$

b $=$ Matrix$(\text{'}$b$\text{'},[[1,2],[3,4]])$

print$(\text{'}$printing a$-$b$\text{'})$

print$($a$-$b$)$

Example $3$ Output:

printing a$-$b

a$-$b$=$

$86$

$42$

Example $4$ Code:

a $=$ Matrix$(\text{'}$a$\text{'},[[1,2],[3,4]])$

a$+1$

print$($a$)$

Example $4$ Output:

a$=$

$23$

$45$

Example $3$ Code:

a $=$ Matrix$(\text{'}$a$\text{'},[[9,8],[7,6]])$

b $=$ Matrix$(\text{'}$b$\text{'},[[1],[3]])$

print$(\text{'}$printing a$-$b$\text{'})$

print$($a$-$b$)$

Example $3$ Output:

printing a$-$b

error