Use Row Reduction to Find the Inverse of the Given $\left[ \begin{array} { c c c } 1 & 9 & 10 \\0 & 9 & 10 \\1 & 0 & 1\end{array} \right]$

question 100

Multiple Choice

Use row reduction to find the inverse of the given matrix, if it exists. Check your answer by multiplication.
$\left[ \begin{array} { c c c } 1 & 9 & 10 \\0 & 9 & 10 \\1 & 0 & 1\end{array} \right]$

• A) \(\left[ \begin{array} { c c c }
• - \frac { 10 } { 9 } & - 1 & \frac { 10 } { 9 } \\
• - 1 & 1 & - 1
• \end{array} \right]\)
• B) \(\left[ \begin{array} { c c c }
• \frac { 10 } { 9 } & - 1 & - \frac { 10 } { 9 } \\
• - 1 & 1 & 1
• \end{array} \right]\)
• C) \(\left[ \begin{array} { c c c }
• - \frac { 10 } { 9 } & - 1 & \frac { 10 } { 9 } \\
• 1 & 1 & - 1
• \end{array} \right]\)
• D) \(\left[ \begin{array} { c c c }
• 1 & 9 & - 10 \\
• 0 & 9 & - 10 \\
• 1 & 0 & 1
• \end{array} \right]\)
• E) The inverse matrix does not exist.

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Definitions:

Sectioned

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A structure, series, or process the end of which is connected to the beginning.

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Load applied along or parallel to the main axis of an object, typically leading to compressive or tensile stress.