We will caluclate the cost per gallon first. Then, we will multiply the new quantity by this cost, so we get the new cost.
As we are told that 6 gallons costs 26.58, we can divide 26.58 by 6 to calculate the cost per gallon. It would be
Now we multiply this quantity by 18, so we get the cost of 18 gallons. It would be
so the cost of 18 gallons is 79.74
Answer: The answers are given below.
Step-by-step explanation: Given that a 3 × 3 matrix P satisfies the matrix equation P² = P.
We are to
(a) find the possibilities for the determinant of P.
(b) explain the reason behind there are no other possibilities.
(c) give an example of P, for each possible determinant.
(a) According to the given information, we have
So, P can be either a zero matrix of order 3 or an identity matrix of order 3.
If P = 0, then det(P) = 0 and if P = I, then det(P) = 1.
Therefore the possible determinants of P are 0 and 1.
(b) There can be any other determinant other than 0 and 1, because if so, then the given equation P² = P will not be satisfied.
(c) If |P| = 0, then the matrix P can be can be of the form as follows:
If |P| = 1, the the matrix P can be of the form as follows :
Thus, all the parts are answered.