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線性代數›Ch4 線性轉換
第 12 題／共 16 題
◀ LA 12/16
12. Matrix Representation、Change of Basis
#LA-04-012易Matrix RepresentationChange of Basis
題組題幹（本題：21，共 5 小題）點擊展開

Suppose β={b1,b2}\beta = \{\mathbf{b}_1, \mathbf{b}_2\} is a basis for VV and C={c1,c2,c3}C = \{\mathbf{c}_1, \mathbf{c}_2, \mathbf{c}_3\} is a basis for WW. Let T:V→WT: V \rightarrow W be a linear transformation with the standard matrix AA for TT. If

β={[1−2],[34]},C={[1−1−3],[−349],[2−24]},A=[111111]\beta = \left\{\begin{bmatrix} 1 \\ -2 \end{bmatrix}, \begin{bmatrix} 3 \\ 4 \end{bmatrix}\right\},\quad C = \left\{\begin{bmatrix} 1 \\ -1 \\ -3 \end{bmatrix}, \begin{bmatrix} -3 \\ 4 \\ 9 \end{bmatrix}, \begin{bmatrix} 2 \\ -2 \\ 4 \end{bmatrix}\right\},\quad A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \\ 1 & 1 \end{bmatrix}

Find the transformation matrix MM for TT relative to β\beta and CC.

1, 2, 4 are in the M matrix.

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