, , , and and will get +1 mark; choosing ONLY M is invertible

, and and will get +2 marks; choosing ONLY and will get +1 mark; choosing ONLY There exists a nonzero column matrix such that

and The set {X R 3 : MX = 0} {0}, where 0=

. ONE OR MORE THAN ONE of these four option(s) is (are) correct answer(s). • For each question, choose the option(s) corresponding to (all) the correct answer(s). • Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 ONLY if (all) the correct option(s) is(are) chosen; Partial Marks : +3 If all the four options are correct but ONLY three options are chosen; Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct; Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option; Zero Marks : 0 If unanswered; Negative Marks : -2 In all other cases. • For example, in a question, if are the ONLY three options corresponding to correct answers, then choosing ONLY will get +4 marks; choosing ONLY will get +2marks; choosing ONLY will get +2 marks; choosing ONLY will get +1 mark; choosing no option(s) (i.e. the question is unanswered) will get 0 marks and choosing any other option(s) will get -2 marks. Let M = (a ij ), i,j {1, 2, 3}, be the 3 x 3 matrix such that a ij = 1 if j + 1 is divisible by i, otherwise a ij = 0. Then which of the following statements is (are) true ? The matrix (M – 2I) is invertible, where I is the 3 x 3 identity matrix