the sum of two numbers is 34. 1/2 the first number plus 1/3 of the second number is 14. write a system to find the numbers. solv
1 answer:
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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.
Answer:
P(X<3) = 0.01004
Step-by-step explanation:
From the given information:
Consider the application of Poisson distribution with the parameter
;
Therefore, we can calculate the required probability as follows:
P(X< 3) = P(X = 0) + P(X = 1) + P(X =2)
P(X<3) = 0.01004