Question

(1 point) Let B be the basis of $\mathbb{R}^2$ consisting of the vectors \begin{equation} \left\{ \begin{bmatrix} 4 \\ 1 \end{bmatrix}, \begin{bmatrix} -1 \\ 3 \end{bmatrix} \right\}, \end{equation} and let C be the basis consisting of \begin{equation} \left\{ \begin{bmatrix} -2 \\ 1 \end{bmatrix}, \begin{bmatrix} 3 \\ -2 \end{bmatrix} \right\}. \end{equation} Find a matrix $P$ such that $[\vec{x}]_C = P[\vec{x}]_B$ for all $\vec{x}$ in $\mathbb{R}^2$. \begin{equation} P = \begin{bmatrix} 5 & 3 \\ -1 & 2 \end{bmatrix} \end{equation} LS: Given a vector $\vec{v} \in \mathbb{R}^n$ ($n = 1, 2$ or 3) and bases $B_1, B_2$ of $\mathbb{R}^n$, I can visualize $[\vec{v}]_{B_1}$ and $[\vec{v}]_{B_2}$.

          (1 point) Let B be the basis of $\mathbb{R}^2$ consisting of the vectors \begin{equation*} \left\{ \begin{bmatrix} 4 \\ 1 \end{bmatrix}, \begin{bmatrix} -1 \\ 3 \end{bmatrix} \right\}, \end{equation*} and let C be the basis consisting of \begin{equation*} \left\{ \begin{bmatrix} -2 \\ 1 \end{bmatrix}, \begin{bmatrix} 3 \\ -2 \end{bmatrix} \right\}. \end{equation*} Find a matrix $P$ such that $[\vec{x}]_C = P[\vec{x}]_B$ for all $\vec{x}$ in $\mathbb{R}^2$. \begin{equation*} P = \begin{bmatrix} 5 & 3 \\ -1 & 2 \end{bmatrix} \end{equation*} LS: Given a vector $\vec{v} \in \mathbb{R}^n$ ($n = 1, 2$ or 3) and bases $B_1, B_2$ of $\mathbb{R}^n$, I can visualize $[\vec{v}]_{B_1}$ and $[\vec{v}]_{B_2}$.

$(1 point) Let B be the basis of ℝ^2 consisting of the vectors { , }, and let C be the basis consisting of { , }. Find a matrix P such that [x⃗]C = P[x⃗]B for all x⃗ in ℝ^2. P = LS: Given a vector v⃗∈ℝ^n (n = 1, 2 or 3) and bases B1, B2 of ℝ^n, I can visualize [v⃗]B1 and [v⃗]B2.$

Added by Andrew G.

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