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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.
Tia went home and said to her mom,"I learned that 10 to the power of 4 is the same as 40,000."
Tia made a mistake in her thinking. Exponent represents the number of zeros.
means we multiply 10 four times
For exponent 4, we put 4 zeros. So answer is 10,000.
Answer:
The length of AB is units
Step-by-step explanation:
The rule of the distance between two points (x1, y1) and (x2, y2) is
∵ The endpoints of AB are (-4, 5) and (2, -7)
→ Let point (-4, 5) be (x1, y1) and point (2, -7) be (x2, y2)
∴ x1 = -4 and y1 = 5
∴ x2 = 2 and y2 = -7
→ Substitute them in the rule above to find the length of AB
∵
∴
∴
∴ The length of AB is units