Solved: Let T be a linear transformation from M2,2 into

Chapter 6, Problem 56

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Let T be a linear transformation from \(M_{2,2}\) into \(M_{2,2}\) such that

\(\begin{array}{l} T\left(\left[\begin{array}{ll} 1 & 0 \\ 0 & 0 \end{array}\right]\right)=\left[\begin{array}{rr} 1 & -1 \\ 0 & 2 \end{array}\right], \quad T\left(\left[\begin{array}{ll} 0 & 1 \\ 0 & 0 \end{array}\right]\right)=\left[\begin{array}{ll} 0 & 2 \\ 1 & 1 \end{array}\right], \\ T\left(\left[\begin{array}{ll} 0 & 0 \\ 1 & 0 \end{array}\right]\right)=\left[\begin{array}{ll} 1 & 2 \\ 0 & 1 \end{array}\right], \quad T\left(\left[\begin{array}{ll} 0 & 0 \\ 0 & 1 \end{array}\right]\right)=\left[\begin{array}{rr} 3 & -1 \\ 1 & 0 \end{array}\right] . \\ \text { Find } T\left(\left[\begin{array}{rr} 1 & 3 \\ -1 & \end{array}\right]\right) . \end{array} \)

Text Transcription:

T([_0^1 _0^1]) = [_0^1 _2^-1], T ([_0^0 _0^1]) = [_1^0 _1^2], T_([_1^0 _0^0]) = [_0^1 _1^2], T([_0^0 _1^0]) = [_1^3 _0^-1]. Find T[(_-1^1 _4^3]).

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