Answer:
Step-by-step explanation:
Given that A is a square matrix and A is idempotent
Consider I-A
i) 
It follows that I-A is also idempotent
ii) Consider the matrix 2A-I
So it follows that 2A-I matrix is its own inverse.
Answer:
The third book cost $9.03
Step-by-step explanation:
Heya !
Using a theoram about triangles ,
Given a triangle ∆ABC, the sum of the lengths of any two sides of the triangle is greater than the length of the third side ,
Also , the length of third side always greater than absolute difference of the other two sides ,
Let the third side be x ,
So , x < 9 + 8 and x > 9 - 8
x < 17 and x > 1
Hence , x ∈ [ 2 , 17 ] inch.
Above case is true for any triangle , be it scalene , Isosceles , Right-angled ...
As , for Isosceles , the third side can be 8 or 9 inches ,
For scalene , all values in the above range satusfies ,
For right angled triangle , we have 2 cases ,
Case 1 : Third side is the hypotenuse
Then , x = √(9²+8²) = √145 = 12.0415 inch.
Case 2 : Third side is not the hypotenuse
Then , x = √(9²-8²) = √17 = 4.1231 inch.
Hope it helps you ! :)
Just solve the equation, x + 0.15x + 0.06x = 15
1.21x = 15,
x = $12.39 (nearly)
