ok, so i know this math problem should be easy, but i really dont understand it. pls help me out!
the following are supposed to be matrices but i do not know how to make them on the computer.
Let X= (1 1
Let Y= (1 -1
Calculate X^2, X^3, X^4, Y^2, Y^3, Y^4
By considering integer powers of X and Y, find expressions for Z^n, Y^n, (X+Y)^n
Let A= aX and B=bY where a and b are constants
Use different values of a and b to calculate A^2, A^3, A^4, B^2, B^3, B^4
By considering interger powers of A and B, find expressions for A^n, B^n, (A+B)^n
Now consider M= (a+b a-b
Show that M= A+B and that M^2= A^2+B^2
Hence, find the general statement that expresses M^n in terms of aX and bY
Test the validity of your general statement by using different Values of a, b, n
Discuss the scope and limitations of your general statement
Use an algebraic method to explain how you arrived at your general statement.
Thanks so mcuh for your help!