Perform the Sequence of Row Operations on the Following Matrix $\left[ \begin{array} { c c c } 1 & 3 & 4 \\3 & - 1 & - 5 \\4 & 1 & - 1\end{array} \right]$

question 72

Multiple Choice

Perform the sequence of row operations on the following matrix. Add -3 times R₁ to R₂.
$\left[ \begin{array} { c c c } 1 & 3 & 4 \\3 & - 1 & - 5 \\4 & 1 & - 1\end{array} \right]$

• A) \(\left[ \begin{array} { c c c }
• 1 & 3 & 4 \\
• 0 & 4 & - 17 \\
• 4 & 1 & - 1
• \end{array} \right]\)
• B) \(\left[ \begin{array} { c c c }
• 1 & 3 & 4 \\
• 0 & - 10 & - 17 \\
• 4 & 1 & - 1
• \end{array} \right]\)
• C) \(\left[ \begin{array} { c c c }
• 1 & 3 & 4 \\
• 0 & - 10 & 3 \\
• 4 & 1 & - 1
• \end{array} \right]\)
• D) \(\left[ \begin{array} { c c c }
• - 1 & 3 & 4 \\
• 0 & - 10 & - 17 \\
• 4 & - 1 & - 1
• \end{array} \right]\)
• E) \(\left[ \begin{array} { c c c }
• 1 & 3 & 4 \\
• 0 & 1 & - 17 \\
• 4 & 1 & - 1
• \end{array} \right]\)

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Definitions:

P(A)

The probability of event A occurring, in the context of all possible outcomes.

P(B)

The probability of event B occurring in a statistical experiment.

Independent Events

Two events that have no influence on each other's occurrence, meaning the probability of one does not affect the other.

P(A And B)

The probability that events A and B both occur, which can be calculated directly or via the multiplication rule for independent events.