Write the System of Equations in Matrix Form $$\left\{ \begin{array} { l } a - b + c = 8 \\4 a - b + c = 0 \\a + b + 2 c = 7 \\a + c + d = 0\end{array} \right.$$

question 91

Multiple Choice

Write the system of equations in matrix form. $$\left\{ \begin{array} { l } a - b + c = 8 \\4 a - b + c = 0 \\a + b + 2 c = 7 \\a + c + d = 0\end{array} \right.$$

• A) \(\left[ \begin{array} { c c c c } 1 & - 1 & 1 & 0 \\ 4 & - 1 & 1 & 0 \\ 1 & 1 & 2 & 0 \\ 1 & 0 & 1 & 1 \end{array} \right] \left[ \begin{array} { l } a \\ b \\ c \\ a \end{array} \right] = \left[ \begin{array} { l } 8 \\ 0 \\ 7 \\ 0 \end{array} \right] \quad\)
• B) \(\left[ \begin{array} { c c c c } 8 & - 1 & 1 & 0 \\ 0 & - 1 & 1 & 0 \\ 7 & 1 & 2 & 0 \\ 0 & 0 & 1 & 1 \end{array} \right] \left[ \begin{array} { l } a \\ b \\ c \\ a \end{array} \right] = \left[ \begin{array} { l } 1 \\ 4 \\ 1 \\ 1 \end{array} \right]\)
• C) \(\left[ \begin{array} { l l l l } 8 & 1 & 1 & 0 \\ 0 & 4 & 1 & 0 \\ 7 & 1 & 2 & 0 \\ 0 & 1 & 1 & 1 \end{array} \right] \left[ \begin{array} { l } a \\ b \\ c \\ a \end{array} \right] = \left[ \begin{array} { l } 0 \\ 0 \\ 0 \\ 1 \end{array} \right]\)
• D) \(\left[ \begin{array} { c c c } 1 & - 1 & 1 \\ 4 & - 1 & 1 \\ 1 & 1 & 2 \end{array} \right] \left[ \begin{array} { l } a \\ b \\ c \end{array} \right] = \left[ \begin{array} { l } 8 \\ 0 \\ 7 \end{array} \right]\)
• E) none

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Definitions:

Market System

A market system is an economic system in which decisions regarding investment, production, and distribution are based on supply and demand, and prices are determined in a free price system.

Property Rights

Property rights are the legal rights to use, control, and dispose of property, including land, buildings, or intellectual property.

Central Planning

A system where a nation's government makes all decisions regarding the economy, including resources allocation and production levels.

Unselfish Behavior

Actions that prioritize the welfare of others over one's own personal benefit.