A directory of Objective Type Questions covering all the Computer Science subjects. Here you can access and discuss Multiple choice questions and answers for various compitative exams and interviews.

 131. Consider the following matrix A. If the eigenvalues of A are 4 and 8, then a. x=4, y=10 b. x=5, y=8 c. x=-3, y=9 d. x=-4, y=10

 132. How many of the following matrices have an eigenvalue 1? a. one b. two c. three d. four

 133. If the matrix A is such that, then the determinant of A is equal to a. 0 b. 1 c. 2 d. 3

 134. The product of the non-zero eigenvalues of the matrix1 0 0 0 10 1 1 1 00 1 1 1 00 1 1 1 01 0 0 0 1is ______ a. 4 b. 5 c. 6 d. 7

 135. Which one of the following statements is TRUE about every n×n matrix with only real eigenvalues? a. If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative. b. If the trace of the matrix is positive, all its eigenvalues are positive. c. If the determinant of the matrix is positive, all its eigenvalues are positive. d. If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
 View Answer Report Discuss Too Difficult! Search Google Answer: (a).If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative.

 136. Consider the set H of all 3 × 3 matrices of the following type, where a, b, c, d, e and f are real numbers and abc ≠ 0. Under the matrix multiplication operation, the set H is a. a group b. a monoid but not a group c. a semigroup but not a monoid d. neither a group nor a semigroup

 137. Consider the following system of equations in three real variables x1, x2 and x3:2x1 - x2 + 3x3 = 1 3x1- 2x2 + 5x3 = 2-x1 + 4x2 + x3 = 3 This system of equations has a. no solution b. a unique solution c. more than one but a finite number of solutions d. an infinite number of solutions