Determine the Inverse of the Given Matrix, If Possible $A=\left[\begin{array}{rrrr}-5 & 5 & 3 & -4 \\0 & 1 & -2 & 0 \\3 & 2 & 1 & 3 \\0 & 1 & 1 & 0\end{array}\right]$

question 37

Multiple Choice

Determine the inverse of the given matrix, if possible. Otherwise, state the matrix is singular.
- $A=\left[\begin{array}{rrrr}-5 & 5 & 3 & -4 \\0 & 1 & -2 & 0 \\3 & 2 & 1 & 3 \\0 & 1 & 1 & 0\end{array}\right]$

• A)\(A^{-1}=\left[\begin{array}{rrrr}
• -1 & -\frac{10}{9} & -\frac{4}{3} & -\frac{59}{9} \\
• 0 & -\frac{1}{3} & 0 & -\frac{2}{3} \\
• 0 & \frac{1}{3} & 0 & -\frac{1}{3} \\
• 1 & \frac{11}{9} & \frac{5}{3} & \frac{64}{9}
• \end{array}\right]\)
• B)\(A^{-1}=\left[\begin{array}{rrrr}
• -1 & \frac{10}{9} & -\frac{4}{3} & \frac{59}{9} \\
• 0 & \frac{1}{3} & 0 & \frac{2}{3} \\
• 0 & -\frac{1}{3} & 0 & \frac{1}{3} \\
• 1 & -\frac{11}{9} & \frac{5}{3} & -\frac{64}{9}
• \end{array}\right]\)
• C)\(\text { Singular matrix }\)
• D)\(A^{-1}=\left[\begin{array}{cccc}
• 1 & \frac{10}{9} & \frac{4}{3} & \frac{59}{9} \\
• 0 & \frac{1}{3} & 0 & \frac{2}{3} \\
• 0 & -\frac{1}{3} & 0 & \frac{1}{3} \\
• -1 & -\frac{11}{9} & -\frac{5}{3} & -\frac{64}{9}
• \end{array}\right]\)

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