G and I are siblings as they share the same parents, H.

g(-1) = 3(-1) + 2 = -3 + 2 = -1.

The determinant of H is calculated as (0*-0) - (1*-1) = 0 + 1 = 1.

Det(H) = (1*-1) - (1*1) = -1 - 1 = -2.

The determinant of H is calculated as 1(1*1 - 0*1) - 2(0*1 - 0*2) + 1(0*1 - 1*2) = 1 - 0 - 2 = -1.

Using the determinant formula for 3x3 matrices, det(H) = 1(1*0 - 4*6) - 2(0 - 4*5) + 3(0 - 1*5) = 0 - 40 - 15 = -55.

The determinant of H is (1*4) - (2*2) = 4 - 4 = 0.

The rank of H is 1 because the second row is a multiple of the first row.

Det(H) = (2*5) - (3*4) = 10 - 12 = -2.

Det(H) = (2*5) - (3*4) = 10 - 12 = -2.

The eigenvalues are found by solving the characteristic equation: det(H - λI) = 0, which gives λ^2 - 9λ + 1 = 0.

The number of ways to choose 2 elements from 3 is given by the combination formula C(3, 2) = 3.

The total number of subsets is 2^3 = 8. Subtracting the empty set gives 8 - 1 = 7.

The power set of H is {∅, {x}, {y}, {x, y}}. The subsets of H are {∅, {x}, {y}}.

Since H is across from I and J is next to H, J is not next to I.

H is the sister of I, and since I is the mother of J, H is the aunt of J.

Using the chain rule, h'(x) = 2e^(2x).

h'(x) = 3x^2 - 3 = 0 gives x^2 = 1, so x = 1 and x = -1 are critical points.

h(1) = 1^3 - 3(1) + 2 = 1 - 3 + 2 = 0.

h(1) = 1^3 - 3*1 = 1 - 3 = -2.

The union of two sets will always have at least as many elements as the larger of the two sets, including unique elements.

Hybrid sets can help reduce redundancy by combining different categories of data into a single representation.

I · J = 1*2 + 1*2 + 1*2 = 2 + 2 + 2 = 6.

I · J = 1*3 + 2*2 + 3*1 = 3 + 4 + 3 = 10.

I · J = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

I · J = 2a + 2b + 2c = 12 gives the equation 2a + 2b + 2c = 12.

Using cofactor expansion, det(I) = 1(1*4 - 3*0) - 0 + 2(0*0 - 1*1) = 4 - 2 = 2.

Using the determinant formula for 3x3 matrices, det(I) = 1(1*0 - 3*1) - 0(0 - 3*1) + 2(0 - 1*1) = 0 - 0 - 2 = -2.

The rank of I is 1 because all rows are linearly dependent.

Using the determinant formula for 3x3 matrices, det(I) = 1(1*0 - 4*6) - 2(0 - 4*5) + 3(0 - 1*5) = 0 - 40 - 15 = -55.