Last Tuesday, a parking lot had 80 cars. Of those 80 cars, 40% were tan, 20 were silver, and the rest were black. What perc
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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.
Step-by-step explanation:
The operations on functions can be performed as they are performed on polynomials
The addition of functions is used in the given question
Given
We have to find:
So,
Keywords: Functions, operations on functions
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