Question

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 + ai3 and Cj = a1j + a2j + a3j for i = 1, 2, 3 and j = 1, 2, 3.

Match each entry in List-I to the corret entry in List-II.List - I	List - II
(P)	The number of matrices M = ( aij )3×3 with all entries in T such that Ri = Cj = 0 for all i, j, is
(Q)	The number of symmetric matrices M = ( aij )3×3 with all entries in T such that Cj = 0 for all j, is
(R)	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
\left\\{\begin{pmatrix} x \\\ y \\\ z \end{pmatrix}:x,y,z\in \R, M\begin{pmatrix} x \\\ y \\\ z \end{pmatrix}=\begin{pmatrix} a_{12} \\\ 0 \\\ -a_{23} \end{pmatrix}\right\\} is	(3)
(S)	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
	(5)
The correct option is

• A. (P) → (4) (Q) → (2) (R) → (5) (S) → (1)
• B. (P) → (2) (Q) → (4) (R) → (1) (S) → (5)
• C. (P) → (2) (Q) → (4) (R) → (3) (S) → (5)
• D. (P) → (1) (Q) → (5) (R) → (3) (S) → (4)

Answer 1

Answer: (C)

(P) → (2) (Q) → (4) (R) → (3) (S) → (5)

Answer 2

The correct option is (C):(P) → (2) (Q) → (4) (R) → (3) (S) → (5).