Let A be a 2 2 matrix with non-zero entries and let A2-1, where 1 is 2 2 identity matrix. Define Tr(A) =sum of diagonal elements of A and A-determinant of Matrix A Stement-1: Tr(A) = 0 statement-2A-1 (a) Satement-1 is true, Statement 2 is true; Statement 2 is not a correct explanation for 11T'JEE 2010 Statement-1; (b) Statement 1 is true, Statement-2 is false (c) Statement 1 is false, Statement-2 is True (d) Statement-1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1 Let A = (a where a, b, c, d 0 ab+bd = 0 and ac + cd = 0 b(a + d) = 0 and c(a + d) = 0 = A2 = ( a2 + bc ab + bd ac cd bc + d2 (a2 + bc ab + bd ac + cd bc d2 Tr(A) = 0 -(a2 + bc ab + bd ac + cd bcd2 01 So, (b) is the correct Answer.
IIT JEE The number of 3 3 non-singular matrices, with four entries as 1 and all other entries as 0, is (a) 5 (b) 6 (c) at least 7 (d) less than 4 (c) is correct answer 1 are 6 non-singular matrices because 6 blanks will be filled by 5 zeros and 1 one. Similarly, 1 -are 6 non singular matrices. So requierd cases are more than 7, non singular 3 x 3 matrices.
Let a, b, c be such that b(a + c)-0. If b +1 a a+1 a-1 b b+1 b-1 a-1 a +1 IIT JEE 2009 c+1 - 0 then the value of n is: n+2 n+1 cc- c (-1)"2a (-1) 1b (-1) C c1 c+1 (A) zero (B) any even integer (C) any odd integer (D) any integer a 1 b+1 c-1 A+(-1)' a-1 b-l c+1|=0 I+-1)-0 a+1 a-1 a A+(-1)" |b + 1 b-l -bl=0 n = Odd Integer c-1 c+1 c
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