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Let and be the distinct roots of the equation x 2 + x – 1 = 0. Consider the set T = {1, , }. For a 3 × 3 matrix M = (a ij ) 3×3 , define R i = a i1 + a i2 + a i3 and C j = a 1j + a 2j + a 3j for i = 1, 2, 3 and j = 1, 2, 3. Match each entry in List-I to the correct entry in List-II. List-I List-II (P) The number of matrices M = (a ij ) 3×3 with all entries in T such that R i = C j = 0 for all i, j, is (1) 1 (Q) The number of symmetric matrices M = (a ij ) 3×3 with all entries in T such that C j = 0 for all j, is (2) 12 (R) Let M = (a ij ) 3×3 be a skew symmetric matrix such that a ij T for i > j. Then the number of elements in the set 23 12 a 0 a z y x M , R z , y , x : z y x is (3) infinite (S) Let M = (a ij ) 3×3 be a matrix with all entries in T such that R i = 0 for all i. Then the absolute value of the determinant of M is (4) 6 (5) 0 The correct option is
- (P) (4), (Q) (2), (R) (5), (S) (1)
- (P) (2), (Q) (4), (R) (1), (S) (5)
- (P) (2), (Q) (4), (R) (3), (S) (5)
- (P) (1), (Q) (5), (R) (3), (S) (4)
Correct answer: (P) (2), (Q) (4), (R) (3), (S) (5)
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