T(x,y) = (x,y,z) of R^2 --gt; R^3, when z=1. Prove that the

8Sec 2. Gler slingscontinued(6) TCX V - ( X, Y, 2) of IR SIR when ( 6 ) 2 - 1Let ( x, y, / #, ) and ( X2, 72, Z 2) be elements of R3 since TIR SRLet k be a scalarT ( ( X , , ) . , 2 ) 4 ( X2 , /2, 2 2 ) = T ( Xity, YIty,, z, 17, ) by vector addition= ( X, t X 2 , Y ty ,Z , 1z , ) by definition of T- (X1, Yl,Zit ( X 2, yz, Z2) by vector AdditionThus, T preserves vector addition= T ( X , , Y , , Z , ) + T ( X ,, Y , , Z, ) by/ definition of TNow, test whether T preserves Scalar multiplicationT ( k ( X , , y , , Z , ) ) = T ( RX, , KY,, KZ, ) by Scalar Multiplication of Vector= (KX, , KY,, KZ. ) by definition of T= k ( X , , Y,, Z, ) by Scalar Multiplication of Vector