Question

Consider the function T: K3 K3 defined by T(x, y, z) = (0, y,0). This kind of function is called a projection, since we are 'projecting' the vector (2, y, z) onto the y-axis. In this problem, you will prove that the function T is linear. In the first part, you will prove that T preserves addition. In the second part, you will prove that T preserves scalar multiplication. There is only one correct answer for each part, so be sure not to skip any steps.

Answer 1

Puadion He have qiven thad a TCa Coz T Preserven additan Let r be aibitary elenents k Then he have TC(x,z)+a2,a)) (o,t ). Co 0) t co ) +TCa Z Theiclare presesve addiHon Scalar Muliplicatian Preserre T 12 and c be arbilaryeemenh a k Let Then He have TCcaa) 1 Cocy00 C CO,,0)

CTCR,Z) Theretore Tpresenves scalar Muliplicaian