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Linear Transformations

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1

Find the standard matrix of the linear transformation T(x,y)=(2x−2y, 2x+3y)T(x, y) = (2x-2y,\ 2x+3y).

A.(−2232)\begin{pmatrix} -2 & 2 \\ 3 & 2 \end{pmatrix}
B.(2−223)\begin{pmatrix} 2 & -2 \\ 2 & 3 \end{pmatrix}
C.(−22−2−3)\begin{pmatrix} -2 & 2 \\ -2 & -3 \end{pmatrix}
D.(22−23)\begin{pmatrix} 2 & 2 \\ -2 & 3 \end{pmatrix}
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2

The linear transformation TT has standard matrix (−25−13)\begin{pmatrix} -2 & 5 \\ -1 & 3 \end{pmatrix}. Compute T(−22)T\begin{pmatrix} -2 \\ 2 \end{pmatrix}.

A.(814)\begin{pmatrix} 8 \\ 14 \end{pmatrix}
B.(148)\begin{pmatrix} 14 \\ 8 \end{pmatrix}
C.(159)\begin{pmatrix} 15 \\ 9 \end{pmatrix}
D.(−14−8)\begin{pmatrix} -14 \\ -8 \end{pmatrix}
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3

Find the standard matrix of the linear transformation T(x,y)=(−4x−4y, −x−3y)T(x, y) = (-4x-4y,\ -x-3y).

A.(−4−1−4−3)\begin{pmatrix} -4 & -1 \\ -4 & -3 \end{pmatrix}
B.(−4−4−1−3)\begin{pmatrix} -4 & -4 \\ -1 & -3 \end{pmatrix}
C.(4413)\begin{pmatrix} 4 & 4 \\ 1 & 3 \end{pmatrix}
D.(−4−4−3−1)\begin{pmatrix} -4 & -4 \\ -3 & -1 \end{pmatrix}
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