Find a Basis for the Set of All Solutions to the Difference

question 27

Multiple Choice

Find a basis for the set of all solutions to the difference equation.
-Let $B = \left\{ \mathbf { b } _ { 1 } , \mathbf { b } _ { 2 } \right\}$ and $C = \left\{ \mathbf { c } _ { 1 } , \mathbf { c } _ { 2 } \right\}$ be bases for $\mathcal { R } ^ { 2 }$ , where
$$\mathbf { b } _ { 1 } = \left[ \begin{array} { l } 2 \\4\end{array} \right] , \mathbf { b } _ { 2 } = \left[ \begin{array} { l } 1 \\3\end{array} \right] , \mathbf { c } _ { 1 } = \left[ \begin{array} { l } 1 \\3\end{array} \right] , \mathbf { c } _ { 2 } = \left[ \begin{array} { r } - 4 \\- 10\end{array} \right]$$
Find the change-of-coordinates matrix from $B$ to $C$ .

• A)
• \(\left[ \begin{array} { r r } 2 & 1 \\ - 1 & 0 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { l l } 0 & - 1 \\ 1 & - 2 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r r } 1 & - 4 \\ 3 & - 10 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { l l } - 2 & 1 \\ - 1 & 0 \end{array} \right]\)

Differentiate between moral hazard and adverse selection.

Identify solutions to mitigate moral hazard in various contexts, such as insurance and employment.

Analyze the implications of moral hazard in insurance settings.

Recognize examples of moral hazard in everyday life and business practices.

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