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:

Bargaining Position

The relative power or leverage that an individual or entity has during negotiation processes.

Outside Options

Alternatives available to negotiators that do not require agreement from the current party they are negotiating with.

Opponent's Options

Potential actions or strategies available to a competitor or adversary.

Sequential Game

A type of game in game theory where players make decisions one after another, allowing for a sequence of actions to unfold.