Determine Whether {V₁, V₂, V₃} Is a Basis for R³

question 30

Multiple Choice

Determine whether {v₁, v₂, v₃} is a basis for R³
-Let $\mathrm { H } = \left\{ \left[ \begin{array} { c } \mathrm { a } + 3 \mathrm {~b} + 4 \mathrm {~d} \\ \mathrm { c } + \mathrm { d } \\ - 3 \mathrm { a } - 9 \mathrm {~b} + 4 \mathrm { c } - 8 \mathrm {~d} \\ - \mathrm { c } - \mathrm { d } \end{array} \right] : a , b , c , \mathrm {~d} \right.$ in $\left. \mathscr { R } \right\}$
Find the dimension of the subspace $\mathrm { H }$ .

• A) \(\operatorname { dim } \mathrm { H } = 2\)
• B) \(\operatorname { dim } \mathrm { H } = 4\)
• C) \(\operatorname { dim } \mathrm { H } = 3\)
• D) \(\operatorname { dim } \mathrm { H } = 1\)

Recognize the role and challenges of behavioral finance vs. traditional financial theories.

Identify the different biases (like overconfidence, conservatism, and regret avoidance) affecting investor behavior.

Comprehend how anomalies and psychological biases lead to market inefficiencies.

Analyze the impact of recent information on investors' decisions and market outcomes.

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Definitions:

Efficient Amount

The optimal level of production or consumption where resources are utilized in the most effective manner without waste.

External Cost

A cost of economic activity not borne by the producer or consumer, but rather by a third party or the environment, often leading to market failure.

Efficient Amount

The quantity of a product or service that achieves a perfect balance between economic efficiency and the satisfaction of all market participants.

Government Intervention

Actions taken by a government to adjust or interfere in the economic affairs of a nation, with the intention of achieving economic or societal objectives.