Question

Is this mapping linear?
L(x1, x2) = (0, x1 + 2, x2)

Answer 1

no its not linear

Answer 2

Thanks, how can you tell?

Answer 3

Use the definition of linear transformation
L(x + y) = L(x) + L(y)
L ( c*x) = c*L(x) , where x,y are vectors

Answer 4

c is a scalar

Answer 5

If you suspect this function is not a linear transformation, you just need to find a specific example that demonstrates the failure of one of the properties.

Answer 6

how about try
x = (1,2)
y= (3,4)
Now show that
L( x + y ) =/= L(x) + L(y) , and you have produced a counterexample.

Answer 7

in other words show that
L( (1+3, 2 + 4) ) =/= L((1,2)) + L((3,4))

Answer 8

another way to prove it, show that
L( 2*(1,1)) =/= 2 * L(1,1)

this might be shorter

Answer 9

Thanks, got it