Write the System of Equations as a Matrix Equation of the Form

question 141

Multiple Choice

Write the system of equations as a matrix equation of the form AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants.
- $$\begin{array} { l } - 5 x - 8 y + 9 z = 16 \\2 x - z = 5 \\- 7 y + z = 8\end{array}$$

• A) \(\left[ \begin{array} { l l l } 5 & 8 & 9 \\ 2 & 0 & 1 \\ 0 & 7 & 1 \end{array} \right] \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { r } 16 \\ 5 \\ 8 \end{array} \right]\)
• B) \(\left[ \begin{array} { r r r } - 5 & - 8 & 9 \\ 2 & - 1 & 0 \\ - 7 & 1 & 0 \end{array} \right] \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { r } 16 \\ 5 \\ 8 \end{array} \right]\)
• C) \(\left[ \begin{array} { r r r } - 5 & - 8 & 9 \\ 2 & 0 & - 1 \\ 0 & - 7 & 1 \end{array} \right] \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { r } - 16 \\ - 5 \\ - 8 \end{array} \right]\)
• D) \(\left[ \begin{array} { r r r } - 5 & - 8 & 9 \\ 2 & 0 & - 1 \\ 0 & - 7 & 1 \end{array} \right] \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { r } 16 \\ 5 \\ 8 \end{array} \right]\)

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Definitions:

Portfolio Beta

A measure of the sensitivity of a portfolio's returns to market returns, representing its relative market risk.

Asset Beta

A measure of the risk of a firm's assets without the impact of debt, used to estimate the cost of equity in the capital asset pricing model (CAPM).

Standard Deviation

A measure of the amount of variation or dispersion of a set of values.