# Thread: matrix powers ... plz help me!!

1. ## matrix powers ... plz help me!!

X = [1 1]
......[1 1]

Y = [1 -1]
.....[-1 1]

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...
By consedering integer powers of A and B, find expression for A^n, B^n , (A+B)^n

2. Hello,

X^2=2X, X^3=(2X)X=2^2X^2,...
Y^2=2E, Y^3=(2E)Y=2Y,...

Now, A^n=(aX)^n=a^nX^n.
For (A+B)^n, compute them for n=2,3,4,... to see what is going on or just use the binomial theorem.

Bye.

3. Originally Posted by wisterville
Hello,

X^2=2X, X^3=(2X)X=2^2X^2,...
Y^2=2E, Y^3=(2E)Y=2Y,...

Now, A^n=(aX)^n=
.
For (A+B)^n, compute them for n=2,3,4,... to see what is going on or just use the binomial theorem.

Bye.
Thanks,
but u wrote, 2^2X^2 , does this means 2^4X ??
can u please show one example?? thanks

4. Hello,

$\displaystyle X^2=2X$,
$\displaystyle X^3=(X^2)X=(2X)X=2(X^2)=2(2X)=2^2X=4X$,
$\displaystyle X^4=(X^3)X=(2^2X)X=2^2(X^2)=2^2(2X)=2^3X=8X$,
$\displaystyle X^5=(X^4)X=(2^3X)X=2^3(X^2)=2^3(2X)=2^4X=16X$,...
To summarize, $\displaystyle X^n=2^{n-1}X$.