Solve the Problem $A = \left[ \begin{array} { r r r } 1 & - 3 & 2 \\ - 2 & 5 & - 1 \\ 3 & - 6 & - 3 \end{array} \right]$

question 61

Multiple Choice

Solve the problem.
-Let $A = \left[ \begin{array} { r r r } 1 & - 3 & 2 \\ - 2 & 5 & - 1 \\ 3 & - 6 & - 3 \end{array} \right]$ 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 \(- b _ { 1 } + b _ { 2 } + b _ { 3 } = 0\).
• B) Equation is consistent for all \(b _ { 1 } , b _ { 2 } , b _ { 3 }\) satisfying \(- 3 b _ { 1 } + b _ { 3 } = 0\).
• C) Equation is consistent for all \(b _ { 1 } , b _ { 2 } , b _ { 3 }\) satisfying \(3 b _ { 1 } + 3 b _ { 2 } + b _ { 3 } = 0\).
• D) Equation is consistent for all possible \(b _ { 1 } , b _ { 2 } , b _ { 3 }\).

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Definitions:

Somatic Nervous System

A segment of the peripheral nervous system that is responsible for voluntary body movements through the control of skeletal muscles.

Messages

Information, ideas, or thoughts conveyed from one entity to another through a specific medium.

Muscles

Tissues in the body that have the ability to contract, enabling movement and force.

Cerebral Cortex

The outer layer of neural tissue of the cerebrum in the brain, playing a key role in memory, attention, perception, awareness, thought, language, and consciousness.