Determine the Number of Solutions to the Augmented Matrix $\left[\begin{array}{rrrrr}1 & 2 & 0 & 1 & 4 \\0 & 1 & -1 & -3 & 2 \\0 & 0 & 1 & 3 & 5 \\0 & 0 & 0 & 0 & 1\end{array}\right]$

question 1

Multiple Choice

Determine the number of solutions to the augmented matrix.
$\left[\begin{array}{rrrrr}1 & 2 & 0 & 1 & 4 \\0 & 1 & -1 & -3 & 2 \\0 & 0 & 1 & 3 & 5 \\0 & 0 & 0 & 0 & 1\end{array}\right]$

• A) infinitely many
• B) 2 solutions
• C) 1 solution
• D) no solutions

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Definitions:

Mesentery

A double layer of peritoneum that attaches the intestines to the wall of the abdomen, providing support and containing blood vessels, nerves, and lymphatics.

Serous Membrane

A thin membrane that lines certain internal cavities, producing serous fluid to reduce friction between internal organs.

Abdominal Organs

The organs within the abdominal cavity, including the stomach, liver, gallbladder, pancreas, intestines, and kidneys.

Diaphragm

A large, dome-shaped muscle located at the base of the lungs and chest that plays a crucial role in breathing.