The Given Set Is a Basis for a Subspace W $x _ { 1 } = \left[ \begin{array} { r } 6 \\ - 3 \\ 0 \end{array} \right] , x _ { 2 } = \left[ \begin{array} { r } 6 \\ - 18 \\ 3 \end{array} \right]$

question 18

Multiple Choice

The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W.
-Let $x _ { 1 } = \left[ \begin{array} { r } 6 \\ - 3 \\ 0 \end{array} \right] , x _ { 2 } = \left[ \begin{array} { r } 6 \\ - 18 \\ 3 \end{array} \right]$

• A)
• \(\left[ \begin{array} { r } 6 \\ - 3 \\ 0 \end{array} \right] , \left[ \begin{array} { r } 18 \\ - 24 \\ 3 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { r } 6 \\ - 3 \\ 0 \end{array} \right] , \left[ \begin{array} { r } - 6 \\ - 18 \\ - 3 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r } - 9 \\ - 3 \\ 0 \end{array} \right] , \left[ \begin{array} { r } 6 \\ - 18 \\ 3 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { r } 6 \\ - 3 \\ 0 \end{array} \right] , \left[ \begin{array} { r } - 6 \\ - 12 \\ 3 \end{array} \right]\)

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Definitions:

Incentive

Motivation or reward offered to encourage specific actions or behaviors.

Motivate Behaviour

The process of stimulating an individual to act in a certain way or to pursue particular goals through internal or external incentives.

External Goal

Objectives or outcomes sought after that exist outside of an individual's internal desires or motivations.

Drive Theory

A psychological theory that posits human behavior is motivated by biological drives that seek homeostasis.