Find the Inverse, If It Exists, for the Matrix $$A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$$

question 52

Multiple Choice

Find the inverse, if it exists, for the matrix.
- $$A=\left[\begin{array}{rrrr}2 & -3 & 0 & 2 \\6 & -6 & 0 & 4 \\6 & -12 & 0 & 6 \\0 & 0 & -2 & 0\end{array}\right]$$

• A)
• \[
• \left[\begin{array}{cccc}
• \frac{1}{2} & -\frac{1}{3} & 0 & \frac{1}{2} \\
• \frac{1}{6} & -\frac{1}{6} & 0 & \frac{1}{4} \\
• \frac{1}{6} & -\frac{1}{12} & 0 & \frac{1}{6} \\
• 0 & 0 & -\frac{1}{2} & 0
• \end{array}\right]
• B)
• \left[\begin{array}{cccc}
• -1 & 1 & 0 & 3 \\
• \frac{1}{2} & 0 & 0 & -\frac{1}{2} \\
• 0 & -\frac{1}{3} & 0 & -\frac{1}{2} \\
• 0 & 0 & -\frac{1}{2} & 0
• \end{array}\right]
• \]
• C)\[
• \left[\begin{array}{cccc}
• -1 & \frac{1}{2} & 0 & 0 \\
• 1 & 0 & -\frac{1}{3} & 0 \\
• 0 & 0 & 0 & -\frac{1}{2} \\
• 3-\frac{1}{2} & -\frac{1}{2} & 0
• \end{array}\right]
• \]
• D) No inverse

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Definitions:

Adhesion Proteins

Proteins involved in the binding of a cell to another cell or to the extracellular matrix, playing critical roles in cell signaling and structure.

Malignant Cells

Abnormal cells that divide uncontrollably and can invade nearby tissues or spread to other parts of the body, forming a cancer.

Anchored

Fixed or firmly attached to a particular position, place, or belief system, preventing movement or change.

Centromere

The region on a chromosome where the two sister chromatids are joined and where the spindle fibers attach during cell division.