The determinant is calculated as \( 1*5 - 2*3 = 5 - 6 = -1 \).

The determinant is calculated as (3*4) - (2*1) = 12 - 2 = 10.

The determinant is calculated as \( 5*8 - 6*7 = 40 - 42 = -2 \).

Calculating gives a determinant of -3.

The inverse of A is A itself since A is an involutory matrix.

The inverse of A is (1/det(A)) * adj(A) = (1/-2) * [[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]].

The vertex form gives the maximum value at x = 2, f(2) = 5.

The vertex form gives the maximum value at x = 3, f(3) = -3^2 + 6*3 - 8 = 4.

The middle term is T(5) = C(8,4) * (2)^4 = 70 * 16 = 1120.

The modulus |z| = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5.

(1 + i)(1 - i) = 1 - i^2 = 1 - (-1) = 2.

(1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 2.

z1 * z2 = (1 + i)(1 - i) = 1 - i^2 = 1 + 1 = 2.

The product of the roots is c/a = -5/2.

Using Vieta's formulas, the product of the roots is 1/2 (c/a = 1/2).

The product of the roots is given by c/a = 2/3.

The product of the roots is given by c/a = 9/3 = 3.

The product of the roots is given by c/a = 8/1 = 8.

The product of the roots is given by c/a = 15/1 = 15.

The range of sin^(-1)(x) is [-π/2, π/2].

The range of y = cos^(-1)(x) is [0, π].

The range of y = sin^(-1)(x) is [-π/2, π/2].

The range of the function y = tan^(-1)(x) is (-π/2, π/2).

The rows of A are linearly dependent, hence the rank is 2.

The rank of the matrix is 2, as the rows are linearly dependent.

The real part of 5 - 7i is 5.

The real part is 2 * cos(π/3) = 2 * 1/2 = 1.

The real part is Re(z) = 4 * cos(π/3) = 4 * 1/2 = 2.

The real part of z = 5 - 2i is 5.

The real part of z = 5 - 4i is 5.