# Solving a matrix equation in Java

I have been trying to implement the given formula in JAVA but i was unsuccessful. Can someone help me find what I am doing wrong? Do i need to shift the summation index and if so how?

My code:

```public final class LinearSystem {

private LinearSystem() {

}

public static int[] solve(int [][]A , int []y) {

int n = A.length;

int[] x = new int[n];

for (int i = 0 ; i < n; i++) {

x[i] = 0;
int sum = 0;

for(int k = i + 1 ; k == n; k++) {
sum +=  A[i][k]*x[k];  //  **java.lang.ArrayIndexOutOfBoundsException: Index 3 out of bounds for length 3**
}

x[i] = 1/A[i][i] * (y[i] - sum);
}

return x;
}

public static void main(String[] args) {

int[][]A = new int[][]{{2,-1,-3},{0,4,-1},{0,0,3}};
int [] y = new int[] {4,-1,23};
System.out.println(Arrays.toString(solve(A,y))); **// awaited result [2, -3, 1]**
}

}
```

Just trying to collect all my comments under the question into one coherent answer, since there are quite a few different mistakes in your program.

1. This method of solving linear equations relies on your calculating the components of the answer in reverse order – that is, from bottom to top. That’s because each `x[i]` value depends on the values below it in the vector, but not on the values above it. So your outer loop, where you iterate over the `x` values needs to start at the biggest index, and work down to the smallest. In other words, instead of being `for (int i = 0; i < n; i++)`, it needs to be `for (int i = n - 1; i >= 0; i++)`.

2. The inner loop has the wrong stopping condition. With a `for` loop, the part between the two semicolons is the condition to continue iterating, not the condition to stop. So instead of `for(int k = i + 1; k == n; k++)`, you need `for(int k = i + 1; k < n; k++)`.

3. You’re doing an integer division at the beginning of `1 / A[i][i] * (y[i] - sum);`, which means the value is rounded to an integer before carrying on. When you divide `1` by another integer, you always get `-1`, `0` or `1` because of the rounding, and that makes your answer incorrect. The fix from point 4 below will deal with this.

4. The formula relies on the mathematical accuracy that comes with working with either floating point types or decimal types. Integers aren’t going to be accurate. So you need to change the declarations of some of your variables, as follows.

```public static double[] solve(double[][] A, double[] y)

double x[] = new double[n];
double sum = 0.0;
```

along with the corresponding changes in the `main` method.

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