Implement the following function to create a matrix of dimensionality numRows x numCols, where matrix starts with an initial size of 0. Furthermore, initialize the value at matrix [i][j] to the product of i and j.

void matrixInit( vector< vector >& matrix, int numRows, int numCols);

For example, if numRows is 3, numCols is 4, you are going to allocate space to matrix so that it contains three row vectors, where the size of each row vector will be 4. At the end of this function call, the content of matrix will be:

size of matrix is: 3x4

matrix[0][0]=0
matrix[0][1]=0
matrix[0][2]=0
matrix[0][3]=0
matrix[1][0]=0
matrix[1][1]=1
matrix[1][2]=2
matrix[1][3]=3
matrix[2][0]=0
matrix[2][1]=2
matrix[2][2]=4
matrix[2][3]=6

Hint: This task requires memory management. Please refer to a C++ reference manual to identify the relevant member functions. Keep in mind that a function such as push_back() also involves memory management.