Find the Inverse of the Given Matrix, If It Exists $\left[ \begin{array} { c c c } 1 & 1 & 1 \\1 & 0 & 5 \\1 & - 1 & 1\end{array} \right]$

question 56

Multiple Choice

Find the inverse of the given matrix, if it exists.
$\left[ \begin{array} { c c c } 1 & 1 & 1 \\1 & 0 & 5 \\1 & - 1 & 1\end{array} \right]$

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

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Definitions:

Podocytes

Specialized cells in the kidneys that wrap around capillaries of the glomerulus, playing a key role in the filtration of blood to form urine.

Vasa Recta

A series of straight capillaries in the kidney that serve as an extension of the loop of Henle, playing a critical role in the concentration of urine.

Nephron Loop

A U-shaped tube in the nephron of the kidney that plays a crucial role in concentrating urine and conserving water.

Proximal Tubule

A major part of the nephron in the kidney, involved in the reabsorption of water, ions, and nutrients from the filtrate and their return to the bloodstream.