Scribd
Upload
90 views1 page

MM 6

The document contains 20 multiple choice questions related to matrices and linear algebra concepts such as eigen values, eigenvectors, rank, nullity, diagonalizability, and matrix multiplication. Some key questions ask about identifying whether a given matrix is symmetric, skew-symmetric, nilpotent, or orthogonal. Other questions test the conditions for matrix multiplication and solving systems of linear equations.

Uploaded by

Somasekhar Chowdary Kakarala
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
90 views1 page

MM 6

The document contains 20 multiple choice questions related to matrices and linear algebra concepts such as eigen values, eigenvectors, rank, nullity, diagonalizability, and matrix multiplication. Some key questions ask about identifying whether a given matrix is symmetric, skew-symmetric, nilpotent, or orthogonal. Other questions test the conditions for matrix multiplication and solving systems of linear equations.

Uploaded by

Somasekhar Chowdary Kakarala
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 1

To get more please visit: www.creativeworld9.blogspot.com 0 6 6 1.

The matrix 6 0 6 is a matrix 6 6 0


(a) Skew-symmetric (b) Symmetric (c) Nilpotent (d) Orthogonal 2 2 2. A = 1 3 1 2 (a) Nilpotent (b) Involutary (c) Orthogonal (d) Idempotent matrix 3x 2 4x 3. Find the value of x such that A is singular were A = 2 2 4 (a) 2 (b) 4 (c) 5 (d) 3 4. If A = 1 0 0 ,B= 1 0 1 1 and C = 0 cos sin then sin cos 2 1 (1 + x) 4 4 is 3

(a) C = A sin - B cos (b) C = A cos + B sin (c) C = A cos - B sin (d) C = A sin + B cos 5. If a matrix A is 4 3 and B is 3 5. The number of multiplication operations needed to calculate the matrix product AB are (a) 64 (b) 65 (c) 60 (d) 61 6. If A
mn

and B

pq

are two matrices, state the condition for the existance of AB+BA

(a) n = p (b) m = p,n = q (c) m = n = p = q (d) q = m 1 0 7. What is the rank of A = 0 1 0 0 (a) 2 (b) 1 (c) 3 (d) 0 8. If 3 4 matrix is of rank 2, then its nullity is (a) 0 (b) 3 (c) 1 (d) 2 9. The system of equations AX = B has no solution if (a) R(AB) = R(A)<n (b) R(AB) = R(A) (c) R(AB) = R(A) (d) R(AB) = R(A)> n 1 2 3 x 4 and X = y then the system L X = 0 has a solution 10. If L = 0 1 0 0 1 z (a) x = 0, y = 0, z = 0 (b) x = -1, y = 1, z = 1 (c) x = 1, y = 1, z = 1 (d) x = 1, y = 1, z = 0 11. X is a characteristic root of A if and only if there exists (a) unit vector (b) Zero vector (c) Negative vector (d) Non zero vector 1 3 4 12. If A = 0 2 6 then the eigen values of A1 are 0 0 5 (a) 1. 2. 5 (b) -1, -1/2, 1/5 (c) 1, 1/2, 1/5 (d) 1, -1/2, 1/5 13. If one of the eigen value is zero, then |A| is (a) zero (b) - |A | (c) non - zero x1 14. If X = x2 be the eigen vector corresponding to the eigen value , then x3 ( A - I) X= (a) 0 (b) - 1 (c) 1 (d) I 15. If X is an eigen vector of A corresponding to an eigen value and k is any non zero scalar, then vector of A for the same eigen value . (a) -kX (b) X (c) kX (d) - X 16. For the square matrix A = (a) 25 I (b) - 10 I (c) 10 I (d) - 25 I 17. If A = (a) (b) (c) (d) 1 2 2 1 , then by Cayley- Hamilton theorem, A8 is 5 4 0 5 , then A2 - 10A = is an eigen (d) unity vector such that A X = X 0 0 1

625 0 0 625 624 0 0 624 623 0 0 623 626 0 0 626 1 1 1 1 is not diagonalizable, why?

18. The matrix A =

(a) real eigen values (b) repeated eigen values (c) no real eigen values (d) zero eigen values 19. If 1 , 2 , 3 are the eigen values of matrix A and An = BDn B 1 then Dn = n 1 0 0 (a) 0 n 0 2 0 0 n 3 n 1 0 0 (b) 0 n 0 2 n 0 0 3 n 1 0 0 (c) 0 n 0 2 0 0 n 3 1 0 0 (d) 0 2 0 0 0 3 20. If X1 = (a) (b) (c) (d) 2 3 2 1 2 3 1 1 3 1 , X2 = 1 1 are the eigen vectors of A , then modal matrix of A is

2 1 3 1 2 1 3 1

You might also like