Find the Inverse, If It Exists, for the Matrix $$\left[ \begin{array} { l l l } 5 & - 2 & 4 \\10 & - 3 & 8 \\5 & - 1 & 4\end{array} \right]$$

question 247

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$\left[ \begin{array} { l l l } 5 & - 2 & 4 \\10 & - 3 & 8 \\5 & - 1 & 4\end{array} \right]$$

• A)
• \[\left[ \begin{array} { l l l }
• \frac { 2 } { 5 } & \frac { 1 } { 5 } & - \frac { 1 } { 2 } \\
• \frac { 1 } { 2 } & \frac { 4 } { 3 } & \frac { 5 } { 8 } \\
• 1 & - 4 & \frac { 1 } { 4 }
• \end{array} \right]\]
• B) The inverse does not exist.
• C)
• \[\left[ \begin{array} { l l l }
• \frac { 1 } { 5 } & \frac { 1 } { 10 } & \frac { 1 } { 4 } \\
• \frac { 1 } { 10 } & - \frac { 1 } { 3 } & \frac { 1 } { 8 } \\
• \frac { 1 } { 5 } & - 1 & \frac { 1 } { 4 }
• \end{array} \right]\]
• D)
• \(\left[\begin{array}{ccc}
• 5 & 10 & 5 \\
• -2 & -3 & -1 \\
• 4 & 8 & 4
• \end{array}\right]\)

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Definitions:

Atomic Orbitals

Mathematical functions describing the probable location of an electron around an atom, instrumental in the formation of chemical bonds.

Sigma Bonding

A type of covalent bond where electrons are shared in an area directly between atoms, involving the overlap of atomic orbitals.

Molecular Orbital

A region in a molecule where an electron is likely to be found, described by a mathematical function reflecting the wave-like properties of electrons.

Cylindrically Symmetric

Refers to objects or systems that have rotational symmetry about a central axis, maintaining the same dimensions in a circular pattern around the axis.