Use Row Reduction to Find the Inverse of the Given $\left[ \begin{array} { c c c c } 1 & 1 & - 1 & 1 \\- 2 & 1 & 1 & 0 \\- 2 & 1 & 0 & 1 \\4 & - 1 & - 1 & - 1\end{array} \right]$

question 70

Multiple Choice

Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication. $\left[ \begin{array} { c c c c } 1 & 1 & - 1 & 1 \\- 2 & 1 & 1 & 0 \\- 2 & 1 & 0 & 1 \\4 & - 1 & - 1 & - 1\end{array} \right]$

• A) \(\left[ \begin{array} { c c c c }
• - 3 & - 4 & 6 & - 1 \\
• 4 & 5 & - 7 & 1 \\
• 5 & 8 & - 11 & 2 \\
• 5 & 7 & - 10 & 2
• \end{array} \right]\)
• B) \(\left[ \begin{array} { c c c c }
• - 3 & 4 & 5 & 5 \\
• - 4 & 5 & 8 & - 1 \\
• 6 & - 7 & - 11 & - 10 \\
• - 1 & 1 & 2 & 2
• \end{array} \right]\)
• C) \(\left[ \begin{array} { c c c c }
• 1 & 0 & - 2 & - 1 \\
• 0 & 1 & 1 & 1 \\
• 2 & 0 & - 5 & - 3 \\
• 2 & - 1 & - 4 & - 3
• \end{array} \right]\)
• D) \(\left[ \begin{array} { c c c c }
• 1 & 0 & 2 & 2 \\
• 0 & 1 & 0 & - 1 \\
• - 2 & 1 & - 5 & - 4 \\
• - 1 & 1 & - 3 & - 3
• \end{array} \right]\)
• E) The inverse matrix does not exist.

---

Definitions:

Form

A structure for collecting or organizing particular data, often used in surveys, tests, or administrative processes.

Formatting

The process of arranging or modifying the appearance of text and graphical elements in a document or presentation, such as alignment, font size, or color.

Design View

A feature in various software applications that allows users to view or modify the layout and graphical elements of a project or document in an intuitive environment.

Form Design

The process of creating the structure, layout, and appearance of interactive forms to collect information from users effectively and efficiently.