Perform the following calculations with the help of the A and b matrices below your student number and the equation Ax=b or (ATA)x=ATb (AT: A transpose of the matrix A). Compare the results of inversion and reduction methods. Also, prepare an integrated C++ software that includes each method and add its codes to your assignment.

1. Calculate the determinant of matrix A.

2. Calculate the trace of the ATA matrix.

3. Calculate the row norms of matrix A.

4. Calculate the column norms of matrix A.

5. Calculate the Euclidean norm (N(A)) of the matrix A.

6. Make sure that N(A)=(track(ATA))^(1/2). 7. Normalize the matrix A according to the Euclidean norm.

8. Calculate the eigenvalues of matrix A.

9. Interpret the instability of matrix A by calculating the Spectral (Todd) condition number. 10. Interpret the instability of matrix A by calculating the Hadamard condition number.

11. Calculate the inverse of matrix A using Kramer's rule.

12. Calculate the inverse of matrix A by pivoting.

13. Calculate the inverse of the A matrix using the Gauss method.

14. Calculate x vector of unknowns with Gaussian algorithm.

15. Calculate the unknowns vector x using the Gauss-Jordan method.

16. Calculate the unknowns vector x with the modernized Gaussian algorithm.

17. Calculate the inverse of the ATA matrix with the modernized Gaussian algorithm.

[ 0.10680.90370.03050.60990.1829 ] [ 0.65380.89090.74410.61770.2399 ] A=[0.49420.33420.50000.85940.8865] [ 0.77910.69870.47990.80550.0287 ] [ 0.71500.19780.90470.57670.4899 ]