Let A be a matrix given by

I a+b 3 1 l

I 0 a-c+3 2 l

I 0 0 d+1 l

where are respectively thedigitsof yourregistration number .

My registration numberis SP19-BCS-030, in that caseandaccordinglythe matrixA will be

I 9 3 1 l

I 0 9 2 l

I 0 0 1 l

First of all write the expression of A corresponding to your registration number. Then answer part 1-17

1. Give all minors of A.

2. Give all co-factors of A.

3. What is the determinant of (-7A).

4. Find adj(A).

5. Write down the characteristic equation of A.

6. Is A singular?

7. Find A4 by using the Cayley-Hamilton's theorem.

8. Find eigenvalues of A.

9. Write down the eigenvectors corresponding to each eigenvalue.

10. Give the eigen-space and eigenvectors corresponding to each eigenvalue ?.

11. Is A diagonalizable?

12. If your answer to part 11 is Yes, then findthenon-singularmatrixPand diagonalmatrixD.

13.Find the null space of A, and hence the nullity.

14. Does the set of all eigenvectors obtained in part 10 span R3?

15. Do the columns of matrix A form an orthogonal basis for R3?

16. If your answer to part 15 is NO? then orthonormalize it using the Gram-Schmidt process.

17. Find norm of A w.r.t. standard inner product on M33 .

18. Find the orthogonal projection of u = (a, b,c) onto v = (c, d,b)

(where a, b , c, d coming from your registration number, as explained earlier)

19. Find distanceand angle betweenvectors u and v, in part 18.

20. Verify Cauchy-Schwarz's inequality for u and v,in part 18.

THIS IS THE COMPLETE QUESTION NOW PLEASE SOLVE THIS AS SOON AS POSSIBLE PLEASE

1. Question the matrix A Is I9 3 1| I0 9 2| I0 0 1| First of all write the expression of A corresponding to your registration number. Then answer part 1- 17 1.. Give all minors of A. 2. Give all co-factors of A. 3. What is the determinant of (-?A). A. Find adle). 5. Write down the characteristic equation of A. 6. Is A singular? Y. Find AA by using the CayieyHamilton's theorem. 8. Find eigenvalues of A. 9'. Write down the eigenvectors corresponding to each eigenvalue. 10. Give the eigen-space and eigenvectors corresponding to each eigenvalue 1. 11. Is A diagonalizable? 12. if your answer to part 11 is Yes. then nd the non-singular matrix P and diagonal matrix D. 13. Find the null space of A. and hence the nullity. 1h. Does the set of all eigenvectors obtained in part 10 span R3? 15. Do the columns of matrix A form an orthogonal basis for R3? 16. If your answer to part 15 is NO? then orthonormalize it using the Gram-Schmidt process. 1?. Find norm of A w. r. t. standard inner product on M13. 13. Find the orthogonal projection of I.I= (a. b. c) onto v = (c. d. b) (where a. b. c. d coming from your registration number. as explained earlier} 19. Find distance and angle between vectors u and v. in part 13. 20. Verify CauchySchwarz's inequality for u and v. in part 18