If Possible,find AB and State the Order of the Result

question 51

Multiple Choice

If possible,find AB and state the order of the result.​ $$A = \left[ \begin{array} { c c c } 5 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & - 3\end{array} \right] , B = \left[ \begin{array} { c c c } 5 & 0 & 0 \\0 & - 5 & 0 \\0 & 0 & 4\end{array} \right]$$ ​

• A) \[\left[ \begin{array} { c c c }
• 25 & 0 & 0 \\
• 0 & - 20 & 0 \\
• 0 & 0 & - 12
• \end{array} \right]\] Order: 3 × 3
• ​
• B) \[\left[ \begin{array} { c c c }
• 23 & 0 & 0 \\
• 0 & - 20 & 0 \\
• 0 & 0 & - 12
• \end{array} \right]\] Order: 3 × 3
• ​
• C) \[\left[ \begin{array} { c c c }
• 27 & 0 & 0 \\
• 0 & - 20 & 0 \\
• 0 & 0 & - 12
• \end{array} \right]\] Order: 3 × 3
• ​
• D) \[\left[ \begin{array} { c c c }
• 21 & 0 & 0 \\
• 0 & - 20 & 0 \\
• 0 & 0 & - 12
• \end{array} \right]\] Order: 3 × 3
• ​
• E) \[\left[ \begin{array} { c c c }
• 29 & 0 & 0 \\
• 0 & - 20 & 0 \\
• 0 & 0 & - 12
• \end{array} \right]\] Order: 3 × 3
• ​

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Definitions:

α

Typically used to denote the level of significance in hypothesis testing, representing the probability of rejecting a true null hypothesis or the threshold of rareness.

β

Often used to represent the slope coefficient in linear regression analysis, indicating the change in the dependent variable for a one-unit change in an independent variable.

Probability

The measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Critical Value

A threshold in hypothesis testing, which the test statistic must exceed in order to reject the null hypothesis, indicating a statistically significant result.