# Linear Algebra - Linear Algebra

61:

Eigen vectors of the matrix

is (are)

 A. (1,0) B. (0,1) C. (1,1) D. (1,-1) Answer Report Discuss Option: D Explanation : Eigen value are roots of the equation i.e. (1 - a)2 - 1 = 0 a2 - 2a = 0 a = 0  or a = 2 when a = 0 this gives x = y when a = 2, This gives x = -y Hence, eigen vectors corresponding to 0 and 2 are  Click on Discuss to view users comments. Write your comments here:
62:

Invers of the matrix

is

 A. B. C. D. Answer Report Discuss Option: C Explanation : For the matrix cofactors are a11= 1, a21 = -5, a12 = -2, a22 = -3 Therefore matrix by cofactors Adjoint A  I A I = -3(1) - 5(2) = -3 - 10  = -13   Click on Discuss to view users comments. Write your comments here:
63:

If A and B are square matrices of size n × 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. Write your comments here:
64:

If A be an invertible matrix and inverse of 7A is

then matrix A is

 A. B. C. D. Answer Report Discuss Option: A Explanation : Inverse of 7A=  = 7 - 8 = -1 Therefore matrices of cofactor and its transpose, Click on Discuss to view users comments. Write your comments here:
65:

If A =

then state transition matrix eAt is

 A. B. C. D. Answer Report Discuss Option: B Explanation : Here,  Click on Discuss to view users comments. Write your comments here: