5. Let $B = \{b_1, b_2\}$ and $C = \{c_1, c_2\}$ be bases for $R^2$. Find the change-of-coordinates matrix from $B$ to $C$ and the change-of-coordinates matrix from $C$ to $B$. Clearly show your work. $b_1 = \begin{bmatrix} 7 \\ 5 \end{bmatrix}$, $b_2 = \begin{bmatrix} -3 \\ -1 \end{bmatrix}$, $c_1 = \begin{bmatrix} 1 \\ -5 \end{bmatrix}$, $c_2 = \begin{bmatrix} -2 \\ 2 \end{bmatrix}$
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Step 1: To find the change-of-coordinates matrix from B to C, we need to express the basis vector of C in terms of the basis vector of B. Show more…
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