# Thread: An uknown in a matrix

1. ## An uknown in a matrix

'Solve for x, when A^4 = C,

A:
( 1 X )
( 0 1 )

and C:
( 1 51 )
( 0 1 )'

At first I took the 4th root of 51, which gave me 2.67,
but when I plotted that into my calculator, it was wrong,
and didn't give me 51.
According to my calculator x = 12.75, but why is that?
12.75 is 51/4, but isn't that wrong since it's A^4?

If anyone understood that and can explain it to me, I'd be very grateful (:

2. Originally Posted by Fnus
'Solve for x, when A^4 = C,

A:
( 1 X )
( 0 1 )

and C:
( 1 51 )
( 0 1 )'

At first I took the 4th root of 51, which gave me 2.67,
but when I plotted that into my calculator, it was wrong,
and didn't give me 51.
According to my calculator x = 12.75, but why is that?
12.75 is 51/4, but isn't that wrong since it's A^4?

If anyone understood that and can explain it to me, I'd be very grateful (:
Do the matrix multiplication:
$A^2 = \left ( \begin{matrix} 1 & 2x \\ 0 & 1 \end{matrix} \right )$

etc.

-Dan

3. Originally Posted by Fnus
'Solve for x, when A^4 = C,

A:
( 1 X )
( 0 1 )

and C:
( 1 51 )
( 0 1 )'

At first I took the 4th root of 51, which gave me 2.67,
but when I plotted that into my calculator, it was wrong,
and didn't give me 51.
According to my calculator x = 12.75, but why is that?
12.75 is 51/4, but isn't that wrong since it's A^4?

If anyone understood that and can explain it to me, I'd be very grateful (:
A^4 =
( 1 4X )
( 0 1 )

(Use matrix multiplication to get AA and then (AA)(AA). There's an interesting pattern due to the special property of A. Do you see it?)

Therefore .......

4. Originally Posted by topsquark
Do the matrix multiplication:
$A^2 = \left ( \begin{matrix} 1 & 2x \\ 0 & 1 \end{matrix} \right )$

etc.

-Dan
I dispensed with the latex pleasantries and you still beat me, dang it!

5. Originally Posted by Fnus
At first I took the 4th root of 51, which gave me 2.67,
but when I plotted that into my calculator, it was wrong,
and didn't give me 51.
12.75 is 51/4, but isn't that wrong since it's A^4?
One very important point you are missing is that A^4 does not mean you are raising all the elements of matrix A to the power 4!

A^4 means A.A.A.A, where . is matrix multiplication. That is you have to multiply A to itself 4 times using matrix multiplication technique.

Now,do you understand why taking 4th root was wrong?

6. Originally Posted by mr fantastic
I dispensed with the latex pleasantries and you still beat me, dang it!
I'm just that good, what can I say?

-Dan

7. Yosh yosh,
now I get it.

Thanks a ton. (: