## Description

The Problem

We are going to work on 2D vectors.

2D vector as a matrix

You remember matrices, do not you? We are going to do some simple manipulation of a matrix, namely: adding two matrices and multiplying a matrix by a scalar. You watched the 2D vector video, right? RIGHT???

Matrix

A **matrix** is a 2-dimensional (rows and columns) data structure. It has a shape indicated by the number of rows and the number of columns. Though I suppose a matrix could have uneven sized rows, this does not usually happen in practice so a matrix is always rectangular, potentially square (based on its shape).

Matrix operations

We will perform two operations on our matrices, yielding a new matrix as a result.

The first is **scalar multiplication**. Regardless of the size or shape, if the matrix is not empty we multiply the scalar value by every entry in the matrix, yielding a new matrix. We do this for every entry in the matrix.

The second is **addition**. The shape of the two matrices **must be the same** for addition to go forward. If the shapes are the same and they are both not empty, we add the same row/col element of each argument matrix into the same row/col element of a new matrix, yielding the new matrix. We do this for every element in the two matrices.

# Requirements

We will use a `vector<vector<long>>` as the underlying representation of our matrix. This means that the top level vector has, as elements, another vector.

In `functions.h` we provide two using definitions to make things a little easier, to wit:

`using matrix_row = vector<long>;`

`using matrix = vector<matrix_row>;`

This is really a big win! We need only say that the type of vector in a `matrix_row` is a `long` and then, if we are careful, can easily change the type of our entire code set by just changing that one template.

Function Declarations

The functions are clearly described in the functions.h file provided, read them there.

Printing

I think printing the 2D matrix is actually kind of hard. Here are some tips to help out:

In the include file `iomanip` is an io manipulator `setw`. It sets the width for an output element:

– Unlike every other manipulator, it requires you to run it each time you use it.

– If you say something like `cout << setw(5) << 123` then 5 spaces are reserved for output, 3 of which are occupied by 123 and two of which are just blank spaces (the default, you can change that with **setfill**)

– Two other manipulators are **left** and **right** for left or right justification respectively. Thus

– `cout << right << setw(5) << 123` prints 2 spaces and 123

– `cout << left << setw(5) << 123` prints 123 and 2 spaces

– If you use an `ostringstream` (and you should) then any `endl` in the stringstream counts as a character in the stream.

– My code used:

– `ostringstream` to capture the output and then convert to a string

– `setw` to set the width, where the default is 3

– `right` to get the elements right justified so they look better

Other Hints

- Write a function, test a function, write the next function, test that function, etc. This is the way you figure things out, one by one.
- You can make a temporary row (of type `matrix_row`) and `push_back` values on to that. You can then `push_back` the row onto a matrix (of type `matrix`). You can reuse the row in the your loop, but remember to `clear()` it first.