Find the sum of the following vectors:

A girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin two times and notes the number of heads obtained. If she obtained exactly two heads, what is the probability that she threw 1, 2, 3 or 4 with the die?

Using the method of integration, find the area of the region bounded by the following lines:

3x - y - 3 = 0

2x + y - 12 = 0

x - 2y - 1 = 0

If write the minor of element a₂₂.

Using properties of determinants, prove the following: