In obtaining the solution of the system of linear equations: x + y + z = 7 x + 2y + 3z = 16 x + 3y + 4z = 22 by Cramer's rule, the value of y is obtained by dividing D2 by D, where D is the determinant of the coefficient matrix. What is the value of the determinant D2?

Let T2 be the set of all 2 × 2 matrices A = a bc d where a, b, c, d ∈ {0, 1, 2, 3, 4, 5, 6}. Find the number of matrices A such that A is either symmetric or skew-symmetric and det(A) is divisible by 7.

If f(x) = [cos x -sin x 0; sin x cos x 0; 0 0 1], then f(x + y) is equal to:

If A = 13 [1 -2 2; -2 1 2; -2 -2 -1], then matrix A is: