Solve the System Using the Inverse That Is Given for the Coefficient

question 25

Multiple Choice

Solve the system using the inverse that is given for the coefficient matrix.
- $x + 2 y + 3 z = - 3$ $x + y + z = 12$ $2 x + 2 y + z = 6$$\quad$ The inverse of $\left[ \begin{array} { l l l } 1 & 2 & 3 \\ 1 & 1 & 1 \\ 2 & 2 & 1 \end{array} \right]$ is $\left[ \begin{array} { r r r } - 1 & 4 & - 1 \\ 1 & - 5 & 2 \\ 0 & 2 & - 1 \end{array} \right]$

• A) \(\{ ( 45 , - 51,18 ) \}\)
• B) \(\{ ( 15 , - 60,15 ) \}\)
• C) \(\{ ( - 12 , - 24,6 ) \}\)
• D) \(\{ ( 51,69,30 ) \}\)

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Definitions:

Standard Deviation

A statistical measure of the dispersion or spread of a set of data points in relation to their mean, used to gauge volatility.

Correlated

Refers to the relationship between two variables where a change in one can be associated with a change in the other.

Market

A place or system where buyers and sellers interact to trade goods, services, or securities.

Expected Return

This refers to the average amount of profit or loss one can expect from an investment based on its historical performance and probabilities of outcomes.