- #1

arhzz

- 236

- 46

- Homework Statement:
- Check if the transformation from R^3 to R^3 is linear

- Relevant Equations:
- Homogen,additiv properties

Hello!

I need to check if this transformation (not sure if it is the right word in English) from ## R^3 to R^3 ## is linear

f(x1,x2,x3) = f(sin(x1),x2+x3,0). Now we are given that the transformation is linear if this you can prove this statement.

$$f(\lambda * u + \mu * v) = \lambda * f(u) + \mu * f(v)$$

Now what confuses me here is what is my u and what is my v? I'd though my u was (x1,x2,x3) and v sas the left brackes so (sin(x1),x2+x3,0) but that doenst seem to make much sence.I've searhed online a bit and I've found no examples of this property that was given to us in class but rathere these propperties.

Homogenous:

$$f(\alpha x) = \alpha f(x)$$

Additive:

$$f(\alpha x + y ) = \alpha f(x) + f(y)$$

Now I am not sure how to approach this,proofs are definately not my thing and I am stuck on what is my u,v or in the cases i found online my,alpha y?

I need to check if this transformation (not sure if it is the right word in English) from ## R^3 to R^3 ## is linear

f(x1,x2,x3) = f(sin(x1),x2+x3,0). Now we are given that the transformation is linear if this you can prove this statement.

$$f(\lambda * u + \mu * v) = \lambda * f(u) + \mu * f(v)$$

Now what confuses me here is what is my u and what is my v? I'd though my u was (x1,x2,x3) and v sas the left brackes so (sin(x1),x2+x3,0) but that doenst seem to make much sence.I've searhed online a bit and I've found no examples of this property that was given to us in class but rathere these propperties.

Homogenous:

$$f(\alpha x) = \alpha f(x)$$

Additive:

$$f(\alpha x + y ) = \alpha f(x) + f(y)$$

Now I am not sure how to approach this,proofs are definately not my thing and I am stuck on what is my u,v or in the cases i found online my,alpha y?