Prove that the given transformation is a linear transformation, using the definition (or the Remark following...

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Prove that the given transformation is a linear transformation, using the definition (or the Remark following Example 3.55). Tis a linear transformation if and only if T(c,v, + czv2) = c, T(v,) + c,T(v,), where v, = v, = Then, entering your answers in terms of c,, C2, X1, X2, Y, and y2 T(c,V1 + c2v2) = + Ca Y2 C, = 1 C2X2 + C2Y2 CX1 - C1Y1 X2 + Y2 = C1 + C2 X1 - Y1 = cT(v,) + c2T(v2) and thus Tis linear. Prove that the given transformation is a linear transformation, using the definition (or the Remark following Example 3.55). Tis a linear transformation if and only if T(c,v, + czv2) = c, T(v,) + c,T(v,), where v, = v, = Then, entering your answers in terms of c,, C2, X1, X2, Y, and y2 T(c,V1 + c2v2) = + Ca Y2 C, = 1 C2X2 + C2Y2 CX1 - C1Y1 X2 + Y2 = C1 + C2 X1 - Y1 = cT(v,) + c2T(v2) and thus Tis linear.