Fill in the Blank Using Elementary Row Operations to Form $$\left[ \begin{array} { r r r } 2 & 1 & - 2 \\- 10 & - 1 & 9\end{array} \right]$$

question 41

Multiple Choice

Fill in the blank using elementary row operations to form a row-equivalent matrix. $$\left[ \begin{array} { r r r } 2 & 1 & - 2 \\- 10 & - 1 & 9\end{array} \right]$$ $$\left[ \begin{array} { l l l } 2 & 1 & - 2 \\0 & \square & - 1\end{array} \right]$$

• A) \[\left[ \begin{array} { c c c }
• 2 & 1 & - 2 \\
• 0 & - 6 & - 1
• \end{array} \right]\]
• B) \[\left[ \begin{array} { l l l }
• 2 & 1 & - 2 \\
• 0 & 4 & - 1
• \end{array} \right]\]
• C) \[\left[ \begin{array} { r r r }
• 2 & 1 & - 2 \\
• 0 & - 4 & - 1
• \end{array} \right]\]
• D) \[\left[ \begin{array} { l l l }
• 2 & 1 & - 2 \\
• 0 & 1 & - 1
• \end{array} \right]\] ​
• E) \[\left[ \begin{array} { l l l }
• 2 & 1 & - 2 \\
• 0 & 0 & - 1
• \end{array} \right]\] ​

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Definitions:

Gambler's Fallacy

The erroneous belief that if a particular event occurs more frequently than normal during the past, it is less likely to happen in the future, or vice versa, in situations that are truly random.

Ignoring Base Rates

Ignoring base rates is a cognitive bias that involves disregarding or underestimating general information (base rates) in favor of specific individual information when making decisions or judgments.

Availability Bias

A cognitive bias that causes people to overestimate the likelihood of events based on their availability in memory, often leading to skewed decision-making.

Belief Perseverance

The tendency to cling to one's initial belief even after receiving new information that contradicts or disconfirms the basis of that belief.