Gate Exam

Consider the following statements:
S1: The sum of two singular n x n matrices may be non-singular
S2: The sum of two n x n non-singular matrices may be singular.
Which of the following statements is correct?
(a) 51 and S2 are both true
(b) 51 is true, S2 is false
(c) 51 is false, S2 is true
(d) 51 and S2 are both false

Read Solution (Total 1)

s1 & s2 both are true. option B
11 years agoHelpfull: Yes(0) No(0)

Gate Other Question

X,Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half
a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which
of the following is true?
(a) k must be 1
(b) k must be 0
(c) k can take any value between 0 and 1
(d) None of the above
Visit Consider the following relations:
R1 (a,b) iff (a+b) is even over the set of integers
R2 (a,b) iff (a+b) is odd over the set of integers
R3 (a,b) iff a.b > 0 over the set of non-zero rational numbers
R4 (a,b) iff a + bi 2 over the set of natural numbers
Which of the following statements is correct?
(a) Ri and R2 are equivalence relations, R3 and R4 are not
(b) Ri and R3 are equivalence relations, R2 and R4 are not
(c) Ri and R4 are equivalence relations, R2 and R3 are not
(d) Ri, R2, R3 and R4 are all equivalence relations