Let W Be the Subspace Spanned by the Uʹs A) $$\mathbf { y } = \left[ \begin{array} { r } 6 \\14 \\4\end{array} \right] + \left[ \begin{array} { r } 11 \\- 7 \\8\end{array} \right]$$

question 33

Multiple Choice

Let W be the subspace spanned by the uʹs. Write y as the sum of a vector in W and a vector orthogonal to W.
- $\mathbf { y } = \left[ \begin{array} { r } 17 \\ 7 \\ 12 \end{array} \right] , \mathbf { u } _ { 1 } = \left[ \begin{array} { r } 2 \\ 2 \\ - 1 \end{array} \right] , \mathbf { u } _ { 2 } = \left[ \begin{array} { r } - 1 \\ 3 \\ 4 \end{array} \right]$

• A)
• \[\mathbf { y } = \left[ \begin{array} { r }
• 6 \\
• 14 \\
• 4
• \end{array} \right] + \left[ \begin{array} { r }
• 11 \\
• - 7 \\
• 8
• \end{array} \right]\]
• B) \(y=\left[\begin{array}{r}
• 6 \\
• 14 \\
• 4
• \end{array}\right]+\left[\begin{array}{l}
• 23 \\
• 21 \\
• 16
• \end{array}\right]\)
• C)
• \(\mathbf{y}=\left[\begin{array}{r}
• 12 \\
• 28 \\
• 8
• \end{array}\right]+\left[\begin{array}{r}
• 5 \\
• -21 \\
• 4
• \end{array}\right]\)
• D)
• \(\mathbf{y}=\left[\begin{array}{r}
• 6 \\
• 14 \\
• 4
• \end{array}\right]+\left[\begin{array}{r}
• -11 \\
• 7 \\
• -8
• \end{array}\right]\)

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Definitions:

Hedge Ratio

The proportion of a position or investment that is hedged, aiming to reduce risk exposure.

Hedge Ratio

The ratio that compares the value of the position protected via a hedge to the size of the entire position itself.

Dollar Change

The difference in an asset's price when compared to a previous price, often used to quantify gains or losses in securities.

Hedge Ratio

The ratio of the size of a position in a hedging instrument to the size of the position being hedged, used to minimize risk.