Question

(a) Let [r s] ∈R^2 and T: R2→R2 be defined by T(⃗u)=⃗u+ [r s].
Show that if r /= 0 or s/=0 thenT is not a linear transformation of R^2

(b) i. Let Tr,s : R3 → R3 be the linear transformation defined by
Tr,s ([ x y 1]) = [x + r, y +s, 1])
Write down the matrix of Tr,s. (Note: it is a 3 × 3 matrix.)

ii. Show that Tr,s is an isomorphism of R3.
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