T1,T2 and T3 are three maps defined on R^3 as: T1(x,y,z)=(x+1,y,z), T2(x,y,z)=(xy,,cdot,,z), T3(x,y,z)=(x+y,,y+z,,z+x). Which of these maps are linear?

Q26Section II (Mathematics)26 of 190

Spotting linearity: no constant shifts, no products of coordinates

$T_1,T_2$ and $T_3$ are three maps defined on $\mathbb{R}^3$ as: $T_1(x,y,z)=(x+1,y,z)$ , $T_2(x,y,z)=(xy,\,\cdot\,,z)$ , $T_3(x,y,z)=(x+y,\,y+z,\,z+x)$ . Which of these maps are linear?

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