In this exercise, t: r2 → r2 is a function. for each of the following parts, state why t is not linear. (a) t(a1, a2)= (1, a2) (b) t(a, a2) (a1,ai) (c) t(a1,a2)= (sin a1,0) (d) t(al, aa) = (lal, a2) (e) t(a1, d12) = (a1 + 1, a2)

a) T is not homogeneousb) T is not additivec) T is not homogeneousd) T is not additivee) T is not additive

Step-by-step explanation:

In each case there is an example where one property of linear functions fails.

a) . These vectors are not equal, then T doesn't satisfy the condition of scalar multiplication (homogeneity).b) . Because these vectors are not equal, T doesn't satisfy the property of vector addition (additivity).c) so T is not homogeneous.d) then T is not additive.e) then T is not additive.