Let B and C be the two bases for \(\mathbb{R}^2\) given below. Find \(P_{C \leftarrow B}\), the change-of-coordinates matrix from B to C, and \(P_{B \leftarrow C}\), the change-of-coordinates matrix from C to B. \(B = \begin{bmatrix} 2 \\ 0 \end{bmatrix}, \begin{bmatrix} -2 \\ -1 \end{bmatrix}\) \(C = \begin{bmatrix} 0 \\ 1 \end{bmatrix}, \begin{bmatrix} 2 \\ -1 \end{bmatrix}\) \(P_{C \leftarrow B} = \begin{bmatrix} 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 \end{bmatrix}\) \(P_{B \leftarrow C} = \begin{bmatrix} 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 \end{bmatrix}\)
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To find PcB, we need to express the basis vectors of C in terms of the basis vectors of B. The basis vectors of B are [8], [], and [i]. The basis vectors of C are [3], [], and [0]. To express [3] in terms of [8], [], and [i], we need to find the coefficients a, Show moreβ¦
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