Hello, samanthaj1001!
This will take a while . . . I'll answer this in several sessions . . .
(a)1) Let
(a) Calculate:
(b) By considering integer powers of and , find expressions for
(b)
. . .
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
1 1)
Let Y= (1 -1
-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
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!
Hello again, Samantha!
Let: . .[1]
Now consider: .
(a) Show that: .
From [1], we have: .
Hence: .
(b) Show that: .
. .
. .
. . .[2]
. . .
.[3]
Since [2] = [3]: .
(c)Hence, find the general statement that expresses in terms of and
Using a lot of scrap paper, I found that the pattern holds . . .
. .
Therefore: .
Hello again, Samantha!
From [1] we have: .Let
Let: . . [1]
(a) Use different values of to calculate: .
By considering interger powers of , find expressions for: .
We have already worked out the powers of: in a previous segment.
I'll leave the "Test, Discuss, and Explain" portions for you . . .
by the way, i just want to point out that I'm not asking for the answer to my question...it's not that I want the exact answer on how to do it. I just want some hints on how to approach that question or some clarification and guidance on what exactly it is that it is asking. I've done the whole IB internal assesment on my own (unlike some people who are too lazy and just wanted the straight answer so they could copy/paste and hand it in...at least the answer given here helped me check my own work) but I'm stuck on how to work that last one. I would really appreciate some help.