Ononot — Let B1 = \{(1, 0), (0, 1)\} and B2 = \{(2, 1), (1, -1)\} be

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Vectors & Spaceshard

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Let $B_1 = \{(1, 0), (0, 1)\}$ and $B_2 = \{(2, 1), (1, -1)\}$ be two bases for $\mathbb{R}^2$ . If $P = \begin{pmatrix} 2 & 1 \\ 1 & -1 \end{pmatrix}$ is the change-of-basis matrix from $B_2$ to $B_1$ , and $[\mathbf{v}]_{B_2} = (3, 2)^T$ , what is $[\mathbf{v}]_{B_1}$ ?