Consider the following system of equations :

x + 2y $$-$$ 3z = a

2x + 6y $$-$$ 11z = b

x $$-$$ 2y + 7z = c,

where a, b and c are real constants. Then the system of equations :

Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A² is 1, then the possible number of such matrices is :

The value of $$\left| {\matrix{ {(a + 1)(a + 2)} & {a + 2} & 1 \cr {(a + 2)(a + 3)} & {a + 3} & 1 \cr {(a + 3)(a + 4)} & {a + 4} & 1 \cr } } \right|$$ is :

Let A be a 3 $$\times$$ 3 matrix with det(A) = 4. Let R_i denote the i^th row of A. If a matrix B is obtained by performing the operation R₂ $$ \to $$ 2R₂ + 5R₃ on 2A, then det(B) is equal to :