Begginning with multi-dimensional vectors

Hello all,

I am new here to cplusplus.com and I was hoping you guys could answer a question of mine. So I'm very very new to c++, but have had ample experience in PHP, and some Java.

So I have to make this program that asks a user how many rows and columns they would like in an array and then I have to ask them for the numbers they would like to put in that array. Then I have to take those numbers and find which row has the highest sum. I am capable of doing that, but I'm having trouble with getting the structure down.

So I decided I wanted to use vector's since they apparently are much easier to use than array's and here is what I've got :

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#include <iostream>
#include <vector>
using namespace std;

class Calculator
{
    int rows, columns;

    public:
    void GetData()
    {
        cout << "How many rows would you like? ";
        cin>> rows;
        cout << "How many columns would you like? ";
        cin >> columns;
        vector <int> < vector<int> > multiarray(rows, vector<int> columns);
            for (int curRow = 0; curRow < rows; curRow++)
            {
                switch(curRow + 1) {
                case 1:
                    cout << "Please enter numbers for the 1st row : ";
                    break;
                case 2:
                    cout << "Please enter numbers for the 2nd row : ";
                    break;
                case 3:
                    cout << "Please enter numbers for the 3rd row : ";
                    break;
                default:
                    cout << "Please enter numbers for the " << curRow << "th row : ";
                    break;
                }

                for (int arrayPos=0; arrayPos < columns; arrayPos++)
                {
                    cin >> multiarray[curRow][arrayPos];
                }
            }
        CalcMax();
    }

    void CalcMax()
    {

    }
};

int main ()
{
    Calculator calc;
    calc.GetData();
  return 0;
}

I won't even start with the errors that I get when trying to pass the vector, but here are the errors I get when trying to declare the vector: (and yes, I have tried googl'ing and finding the answers, but most of them are way over my head)

error: 'std::vector<int>' is not a template
error: expected primary-expression before 'columns'

It's ok to rip this apart. I know I have to start somewhere, but any way you can help would be great.

Thanks!
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