# Matrices using vectors

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Vectors can be used as a 2D matrix by defining them as a vector of vectors.

A matrix with 3 rows and 4 columns with each cell initialised as 0 can be defined as:

``std::vector<std::vector<int> > matrix(3, std::vector<int>(4));``

The syntax for initializing them using initialiser lists or otherwise are similar to that of a normal vector.

``````std::vector<std::vector<int>> matrix = { {0,1,2,3},
{4,5,6,7},
{8,9,10,11}
};``````

Values in such a vector can be accessed similar to a 2D array

``int var = matrix[0][2];``

Iterating over the entire matrix is similar to that of a normal vector but with an extra dimension.

``````for (int i = 0; i < 3; ++i)
{
for(int j = 0; j < 4; ++j)
{
std::cout << matrix[i][j] << std::endl;
}
}``````
``````for (auto& row: matrix)
{
for(auto& col : row)
{
std::cout << col << std::endl;
}
}``````

A vector of vectors is a convenient way to represent a matrix but it’s not the most efficient: individual vectors are scattered around memory and the data structure isn’t cache friendly.

Also, in a proper matrix, the length of every row must be the same (this isn’t the case for a vector of vectors). The additional flexibility can be a source of errors.