Question

Determine whether each of the linear transformations is linear or not. Check the two conditions of...

Determine whether each of the linear transformations is linear or not. Check the two conditions of linearity.

a) T(x,y,z)=(x,x)

b) T(x,y,z)=(x, x2, x3)

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Answer #1

by definition T is a linear transformation if it satisfies

T(X+Y)=T(X)+T(Y) and T(CX)=CT(X) ,C is a scalar.

a)it is a linear transformation.

b)not a linear transformation.

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