Given is a matrix with elements of the data type double. In order to sum up all matrix elements of the first column, a nested loop has to be used.

This statement is not entirely correct. While you can use a nested loop to sum up all elements of the first column in a matrix, it's not the only way and in many cases, it's not the most efficient way. Here's how you can do it with a single loop:

1. Initialize a variable to hold the sum. You can call it sum and set it to 0.

2. Create a loop that goes through each row in the matrix. You can do this with a for loop. The index in this loop will be the row index.

3. In the loop, add the first element of the current row to the sum. You can access the first element of the current row with matrix[rowIndex][0].

4. After the loop, sum will hold the sum of all elements in the first column.

Here's how it looks in code:

double sum = 0;
for (int i = 0; i < matrix.length; i++) {
    sum += matrix[i][0];
}

In this code, matrix.length gives the number of rows in the matrix, and matrix[i][0] gives the first element in the i-th row. The += operator adds the right-hand side to the left-hand side and assigns the result to the left-hand side, so sum += matrix[i][0] is equivalent to sum = sum + matrix[i][0].

This code assumes that the matrix is not empty and that all rows have at least one element. If that's not the case,