Solve the Problem $A = \left[ \begin{array} { r r r } 1 & - 3 & 2 \\ - 2 & 5 & - 1 \\ 3 & - 4 & 5 \end{array} \right]$

question 35

Multiple Choice

Solve the problem.
-Let $A = \left[ \begin{array} { r r r } 1 & - 3 & 2 \\ - 2 & 5 & - 1 \\ 3 & - 4 & 5 \end{array} \right]$ and $\mathbf { b } = \left[ \begin{array} { l } b _ { 1 } \\ b _ { 2 } \\ b _ { 3 } \end{array} \right]$ .
Determine if the equation $\mathrm { Ax } = \mathrm { b }$ is consistent for all possible $\mathrm { b } _ { 1 } , \mathrm {~b} _ { 2 } , \mathrm {~b} _ { 3 }$ . If the equation is not consistent for all possible $b _ { 1 } , b _ { 2 } , b _ { 3 }$ , give a description of the set of all $\mathbf { b }$ for which the equation is consistent (i.e., a condition which must be satisfied by $b _ { 1 } , b _ { 2 } , b _ { 3 }$ ) .

• A) Equation is consistent for all \(b _ { 1 } , b _ { 2 } , b _ { 3 }\) satisfying \(- 3 b _ { 1 } + b _ { 3 } = 0\).
• B) Equation is consistent for all \(b _ { 1 } , b _ { 2 } , b _ { 3 }\) satisfying \(2 b _ { 1 } + b _ { 2 } = 0\).
• C) Equation is consistent for all possible \(b _ { 1 } , b _ { 2 } , b _ { 3 }\).
• D) Equation is consistent for all \(b _ { 1 } , b _ { 2 }\), \(b _ { 3 }\) satisfying \(7 b _ { 1 } + 5 b _ { 2 } + b _ { 3 } = 0\).

---

Definitions:

Malnourishment

A condition resulting from a lack of essential nutrients in the diet, leading to various health problems including weight loss, muscle wasting, and weakness.

Nasogastric Tube

A medical tube that is inserted through the nose and down into the stomach for feeding or medication administration.

Xiphoid Process

The smallest and lowest part of the sternum (breastbone) that may be felt as a small lump at the lower end of the sternum.

Total Parenteral Nutrition

A method of feeding that bypasses the gastrointestinal tract, delivering nutrients directly into the bloodstream through an intravenous line.