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A linear transformation on the oxy plane is defined by \(P :...

A linear transformation on the oxy plane is defined by P:(x,y)(2x+y,2y). Find P2

A.

[4014]

B.

[4400]

C.

[4004]

D.

[4104]

Correct answer is C

P:(x,y)(2x+y,2y)

p[xy]=[2xy02y]

\therefore p^2 = \begin{bmatrix} 2&1\\0&-2\end{bmatrix} \begin{bmatrix} 2&1\\0&-2\end{bmatrix} = \begin{bmatrix} 4&0\\0&4\end{bmatrix}