Linear Algebra - Linear Algebra

6:

If A and B are square matrices of size n x n, then which of the following statement is not true?

 A. det. (AB) = det (A) det (B) B. det (kA) = kn det (A) C. det (A + B) = det (A) + det (B) D. det (AT) =1/det (A-1) Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. JAGADEESH said: (3:04am on Saturday 23rd December 2017) }if A={1,2:3,4}= Bdet A=-2det B=-2det (A B)=-8hence proved Write your comments here:
7:

In the matrix equation Px = q. which of the following is a necessary condition for the existence of at least one solution for the unknown vector x?

 A. Augmented matrix [Pq] must have the same rank as matrix P B. Vector q must have only non-zero elements C. Matrix P must be singular D. None of these Answer Report Discuss Option: A Explanation : According to Rouche's theorem, the system is consistent if and only if the coefficient matrix and the augmented matrix K are of the same rank, otherwise the system is inconsistent. Click on Discuss to view users comments. Write your comments here:
8:

Rank of the diagonal matrix

 A. 1 B. 2 C. 3 D. 4 Answer Report Discuss Option: D Explanation : Since the number of non-zero elements on this diagonal matrix is four, hence the rank is four. Click on Discuss to view users comments. Write your comments here:
9:

Matrix, A =

 cosΘ sinΘ 0 sinΘ cosΘ 0 0 0 1

 A. orthogonal B. non-singular C. have A-1 exists D. both (b) & (c) Answer Report Discuss Option: D Explanation : Determinant A = 1 (cos2Θ + sin2Θ) Hence A is non-singular and A-1 exists Click on Discuss to view users comments. hmaza said: (10:19pm on Monday 29th April 2013) singular means det is zero but answer b and c is true Write your comments here:
10:

The matrix B = AT, where A is any matrix is

 A. skew symmetric B. symmetric about the secondary diagonal C. always symmetric D. another general matrix Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Write your comments here: