Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { l l l } 2 & - 5 & 4 \\2 & - 4 & 7 \\4 & - 9 & 11\end{array} \right]$$

question 139

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { l l l } 2 & - 5 & 4 \\2 & - 4 & 7 \\4 & - 9 & 11\end{array} \right]$$

• A)
• \[\left[ \begin{array} { c c c }
• 1 & 0 & \frac { 19 } { 2 } \\
• 0 & 1 & 3 \\
• 0 & - \frac { 1 } { 2 } & 0
• \end{array} \right]\]
• B) The inverse does not exist.
• C)
• \(\left[\begin{array}{lll}
• 2 & 2 & 4 \\
• -5 & -4 & -9 \\
• 4 & 7 & 11
• \end{array}\right]\)
• D)
• \(\left[\begin{array}{lll}
• 1 & 0 & \frac{19}{2} \\
• 0 & 1 & 3 \\
• 0 & 0 & 0
• \end{array}\right]\)

---

Definitions:

Iron

A strong, hard magnetic silvery-gray metal, extensively used in construction and manufacturing, especially as a component of steel.

Isotopes

Atoms of the same element that have the same number of protons but different numbers of neutrons in their nuclei, resulting in different mass numbers.

Bromine

A halogen element with the symbol Br and atomic number 35, known for its reddish-brown color and use in flame retardants and other chemicals.

Isotope

Atoms of the same element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses.