1. Consider the bases \( B=\left\{\mathbf{u}_{1}, \mathbf{u}_{2}\right\} \) and \( B^{\prime}=\left\{\mathbf{u}_{1}^{\prime}, \mathbf{u}_{2}^{\prime}\right\} \) for \( R^{2} \), where \[ \mathbf{u}_{1}=\left[\begin{array}{l}2 \\ 2\end{array}\right], \quad \mathbf{u}_{2}=\left[\begin{array}{r}4 \\ -1\end{array}\right], \mathbf{u}_{1}^{\prime}=\left[\begin{array}{l}1 \\ 3\end{array}\right], \quad \mathbf{u}_{2}^{\prime}=\left[\begin{array}{r}-1 \\ -1\end{array}\right] \] (a) Find the transition matrix from \( B^{\prime} \) to \( B \). (b) Find the transition matrix from \( B \) to \( B^{\prime} \). (c) Compute the coordinate vector \( [\mathbf{w}]_{B} \), where and use (12) to compute \( [\mathbf{w}]_{B^{\prime}} \). (d) Check your work by computing \( [\mathbf{w}]_{B^{\prime}} \) directly.

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Caroline runs a small grocery store. Her customers have been complaining about the lack of organically- grown produce she offers for sale. Caroline believes in sustainability, so she has made the decision to only carry organically grown produce. In addition, she is adding grass-fed beef and organic cage-free chicken products as well. Caroline and her customers would be considered part of the natural market. green market. eco-market.

Subaru launched its Share the Love event in 2008 , partnering with the ASPCA, Make-a-Wish, Meals on Wheels America, and the National Park Foundation. Subaru donates \( \$ 250 \) for each vehicle purchased or leased to the buyer's choice of these charities. Since the launch, Subaru and its participating retailers have donated more than \( \$ 256 \) million and supported over 2,100 hometown charities to help those in need. This is an example of philanthropic marketing. corporate philanthropy. ethical marketing. stakenolder responsibility.