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(Solution Library) Consider the following two bases of R^2: \mathcalB=(1,-2),(3,-4) and \mathcalC=(1,3),(3,8). What are the coordinates of (x, y) relative to

Question: Consider the following two bases of $\mathbb{R}^{2}: \mathcal{B}=\{(1,-2),(3,-4)\}$ and $\mathcal{C}=\{(1,3),(3,8)\}$.

What are the coordinates of $(x, y)$ relative to $\mathcal{B} ?$
What are the coordinates of $(x, y)$ relative to $\mathcal{C} ?$
Find the transition (change-of-basis) matrix from $\mathcal{B}$ to $\mathcal{C}$.
Find the transition (change-of-basis) matrix from $\mathcal{C}$ to $\mathcal{B}$.
What is the relationship between these two matrices?

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(Solution Library) Consider the following two bases of R^2: \mathcalB=(1,-2),(3,-4) and \mathcalC=(1,3),(3,8). What are the coordinates of (x, y) relative to

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