I don't understand it, where I = the identity matrix, why does this work...
(-4I)^503 = -(2^2)503I
You can't just move I outside? Sorry for my ignorance.
I think it is because I doesn't affect anything and can be moved anywhere, since anything multiplied by I is the same thing? I don't know.
I just need someone to clarify me and help me understand what I find difficult (and what you may find easy).
FP1: Any matrices experts? Matrices Problem Watch
- Thread Starter
- 07-04-2013 19:42
- Community Assistant
- 07-04-2013 19:45
- 07-04-2013 19:50
aA x aB = a^2 (A x B)
This is easily seen because you will have a factor of a^2 in each term of each sum that makes up every item in the product.
Through a similar reasoning:
aA x aB x aC = a^3 (A x B x C)
aA x aB x aC x aD = a^4 (A x B x C x D)
(aA)^n = a^n (A^n)
And so, by an application of such:
(aI)^n = (a^n)I^n = (a^n)I
- 07-04-2013 19:52
Also, it kind of makes sense because of how matrix multiplication works and where the 0s are in the identity matrix.