In this assignment you will practice:
You are writing an application that needs to perform basic operations on matrices.
Write a module called matrixops (which you should save in a file called matrixops.py) with the following functions. For each function, be sure to the function design recipe in Practical Programming: An Introduction to Computer Science using Python 3.6, Chapter 3 and summarized in our slides on functions, including the type contract using type hints and a docstring.
matrix_scalar_multMultiplication of a $m \times n$ matrix $\mathbf{A}$ with a scalar number $x$ is defined as follows:
$$ \mathbf{A}x = \left[\begin{array}{cccc} A_{11}x & A_{12}x & \cdots & A_{1n}x \ A_{21}x & A_{22}x & \cdots & A_{2n}x \ \vdots & \vdots & \ddots & \vdots \ A_{m1}x & A_{m2}x & \cdots & A_{mn}x \ \end{array}\right] $$
Write a function named matrix_scalar_mult that takes a matrix parameter named a represented as a list of lists and a number parameter named x, and returns a matrix represented as a list of lists with the same dimensions as a and whose elements are the corresponding elements of a multiplied by x. Assume that a[][] is rectangular -– each row has the same length -– and that a[][]’s dimensions are > 0.
marrix_scalar_opA matrix can be the left operand of the arithmetic operators *, /, +, and - with scalar right operands. Multiplication of a matrix with a scalar we saw above can be generalized for any op as follows:
$$ \mathbf{A} \text{ op } x = \left[\begin{array}{cccc} A_{11} \text{ op } x & A_{12} \text{ op } x & \cdots & A_{1n} \text{ op } x \ A_{21} \text{ op } x & A_{22} \text{ op } x & \cdots & A_{2n} \text{ op } x \ \vdots & \vdots & \ddots & \vdots \ A_{m1} \text{ op } x & A_{m2} \text{ op } x & \cdots & A_{mn} \text{ op } x \ \end{array}\right] $$
Write a function named matrix_scalar_op that takes a matrix parameter named a represented as a list of lists, an op function that takes two numbers and returns a number result (e.g., a function named add that, with the call add(1, 2) would return 3), and a number parameter named x, and returns a matrix represented as a list of lists with the same dimensions as a and whose elements are the corresponding elements of a combined with x using op, that is $a_{ij}$ op x. Assume that a[][] is rectangular – each row has the same length – and that a[][]’s dimensions are > 0.