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Matrices and Determinants

Section: Mathematics

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Question : 5

Total: 56

Let α and β be the distinct roots of the equation x2+x−1=0. Consider the set T={1,α,β}. For a 3×3 matrix M=(aij)3×3), define Ri=ai1+ai2+aβ and Cj=a1j+a2j+a3j for i=1,2,3 and j=1,2,3
Match each entry in List-I to the correct entry in List-II.

The number of matrices M=(aij)3×3 with all entries in T such that Ri=Cj=0 for all i,j is

The number of symmetric matrices M=(aij)3×3 with all entries in T such that Cj=0 for all j is

Let M=(aij)3×3 be a skew symmetric matrix such that aij∈T for i>j . Then the number of elements in the set

):x,y⋅z∈R,M(

Let M=(aij)3×3 be a matrix with all entries in T such that Ri=0 for all i . Then the absolute value of the determinant of M is

The correct option is

[JEE Adv 2024 P1]

(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)

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