The Vector X Is in a Subspace H with a Basis

question 60

Multiple Choice

The vector x is in a subspace H with a basis β = {b₁, b₂}. Find the β-coordinate vector of x.

- $$\mathbf { b } _ { 1 } = \left[ \begin{array} { r } 1 \\- 2\end{array} \right] , \mathbf { b } _ { 2 } = \left[ \begin{array} { r } - 5 \\3\end{array} \right] , \mathbf { x } = \left[ \begin{array} { r } 22 \\- 16\end{array} \right]$$

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

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Definitions:

Deindividuation

A psychological state characterized by decreased self-awareness and diminished social identity, leading to uninhibited and sometimes antisocial behavior.

Social Facilitation

This refers to the improved performance on tasks in the presence of others.

Cheerful

Displaying a happy or lighthearted mood or disposition.

Mood Linkage

Mood linkage refers to the phenomenon where the emotional state of one individual affects and aligns with the emotional state of another individual in a social context.