Inverting a matrix is an advanced interview topic. Today, I am going to explain the steps to reverse a matrix or flip a matrix in C#.

Greetings, Interview Preparation Enthusiasts! Today, we're delving into the realm of matrix inversion, a fundamental concept in linear algebra with significant applications in engineering, physics, and computer science. Join us as we thoroughly examine matrix inversion, accompanied by a practical C# implementation example designed to help you tackle your upcoming coding challenges.

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```
public static double[,] InvertMatrix(double[,] matrix)
{
int n = matrix.GetLength(0);
double[,] augmented = new double[n, n * 2];
// Initialize augmented matrix with the input matrix and the identity matrix
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
augmented[i, j] = matrix[i, j];
augmented[i, j + n] = (i == j) ? 1 : 0;
}
}
// Apply Gaussian elimination
for (int i = 0; i < n; i++)
{
int pivotRow = i;
for (int j = i + 1; j < n; j++)
{
if (Math.Abs(augmented[j, i]) > Math.Abs(augmented[pivotRow, i]))
{
pivotRow = j;
}
}
if (pivotRow != i)
{
for (int k = 0; k < 2 * n; k++)
{
double temp = augmented[i, k];
augmented[i, k] = augmented[pivotRow, k];
augmented[pivotRow, k] = temp;
}
}
if (Math.Abs(augmented[i, i]) < 1e-10)
{
return null;
}
double pivot = augmented[i, i];
for (int j = 0; j < 2 * n; j++)
{
augmented[i, j] /= pivot;
}
for (int j = 0; j < n; j++)
{
if (j != i)
{
double factor = augmented[j, i];
for (int k = 0; k < 2 * n; k++)
{
augmented[j, k] -= factor * augmented[i, k];
}
}
}
}
double[,] result = new double[n, n];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
result[i, j] = augmented[i, j + n];
}
}
return result;
}
```

Step 1 : Matrix Initialization

Initialize the matrix as a 2D array.

Example: A 4x4 matrix with predefined values.

Step 2 : Augmented Matrix Setup

Create an augmented matrix combining the original matrix with an identity matrix.

Example: The left half is the original matrix, and the right half is the identity matrix.

Step 3 : Gaussian Elimination Process

Transform the matrix to its reduced row echelon form by selecting the pivot element and swapping rows if necessary.

Example: Ensure the pivot element is the largest absolute value in the column.

Step 4 : Row Normalization

Normalize the pivot row so that the pivot element becomes 1.

Example: Divide each element of the pivot row by the pivot element.

Step 5 : Column Elimination

Eliminate the other entries in the current column to zero out elements above and below the pivot.

Example: Subtract the appropriate multiple of the pivot row from each other row.

Step 6 : Extracting and Returning the Inverse

Extract the inverse matrix from the augmented matrix.

Example: Copy the right half of the augmented matrix into a separate matrix for the inverse.

## Top comments (3)

easy to understand!

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