Use the Row Reduction Algorithm to Transform the Matrix into Echelon

question 9

Multiple Choice

Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as indicated.
-Find the reduced echelon form of the given matrix. $$\left[ \begin{array} { c r r r r } 1 & 4 & - 5 & 1 & 2 \\2 & 5 & - 4 & - 1 & 4 \\- 3 & - 9 & 9 & 2 & 10\end{array} \right]$$

• A)
• \[\left[ \begin{array} { r r r r r }
• 1 & 0 & 0 & 0 & 26 \\
• 0 & 1 & 0 & 0 & - 8 \\
• 0 & 0 & 0 & 1 & 8
• \end{array} \right]\]
• B) \[\left[ \begin{array} { r r r r r }
• 1 & 4 & - 5 & 1 & 2 \\
• 0 & 1 & - 2 & 1 & 0 \\
• 0 & 0 & 0 & 1 & 8
• \end{array} \right]\]
• C)
• \[\left[ \begin{array} { r r r r r }
• 1 & 4 & - 5 & 0 & - 6 \\
• 0 & 1 & - 2 & 0 & - 8 \\
• 0 & 0 & 0 & 1 & 8
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { r r r r r }
• 1 & 0 & 3 & 0 & 26 \\
• 0 & 1 & - 2 & 0 & - 8 \\
• 0 & 0 & 0 & 1 & 8
• \end{array} \right]\]

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Definitions:

Type I Error

The incorrect rejection of a true null hypothesis, also known as a "false positive" finding in hypothesis testing.

Type II Error

Occurs in hypothesis testing when a false null hypothesis is not rejected, also known as a false negative.

Null Hypothesis

A theory proposing that no meaningful distinction exists between certain groups, attributing any detected variations to random sampling or mistakes in the experiment.

Treatment Population

A group of individuals receiving the treatment or intervention in a study to assess its effectiveness.