Question

Please help me with Linear algebra

Answer 1

Which are linear transformations:

Answer 2

I figured out that the first one is not a lin transformation..

Answer 3

is that right though?

Answer 4

Correct, the sine function makes the first one not a linear transformation.

Answer 5

okay thanks hold up let me try the 2nd one..

Answer 6

how do u prove the 2nd one actually?

Answer 7

We know that when you multiply a vector by a scalar, the scalar can be pulled out of the overall function. So we get: \[(\alpha*x^T)A(\alpha*x)=\alpha^2(x^TAx)\neq \alpha(x^TAx)\]

Answer 8

So wait:
T(ax) = (ax)^tA(ax)+b^t(ax) = a (a x^t A x) + b^t ( x )

Answer 9

aT(x) = a (x^t A x + b^t x) oh I see i'm still missing that a in front of x^t.. so T(ax) is not equal to aT(x).. thanks..

Answer 10

No problem :)

Answer 11

actually can u stand by.. I might have some more questions..

Answer 12

I'll post it as a new thread.. later..

Answer 13

Sure, it's been a while though, so I'm not sure how much help I'll be.