Write the System of Linear Equations as a Matrix Equation $$[ A \mid B ]$$

question 130

Multiple Choice

Write the system of linear equations as a matrix equation AX = B, and use Gauss-Jordan elimination on the augmented matrix $$[ A \mid B ]$$ to solve for the matrix X. $$\left\{ \begin{aligned}x _ { 1 } - 3 x _ { 2 } & = - 25 \\- 5 x _ { 1 } + 2 x _ { 2 } & = 34\end{aligned} \right.$$

• A) \(\left[ \begin{array} { c c }
• 1 & - 3 \\
• - 5 & 2
• \end{array} \right] \left[ \begin{array} { c }
• - 25 \\
• - 4
• \end{array} \right] = \left[ \begin{array} { c }
• 34 \\
• 7
• \end{array} \right]\)
• B) \(\left[ \begin{array} { c c }
• 1 & - 3 \\
• - 5 & 2
• \end{array} \right] = \left[ \begin{array} { c }
• - 25 \\
• 34
• \end{array} \right]\)
• C) \(\left[ \begin{array} { c c }
• 1 & - 3 \\
• - 5 & 2
• \end{array} \right] \left[ \begin{array} { c }
• - 4 \\
• - 25
• \end{array} \right] = \left[ \begin{array} { c }
• 7 \\
• 34
• \end{array} \right]\)
• D) \(\left[ \begin{array} { c c }
• 1 & - 3 \\
• - 5 & 2
• \end{array} \right] \left[ \begin{array} { c }
• - 4 \\
• 7
• \end{array} \right] = \left[ \begin{array} { c }
• - 25 \\
• 34
• \end{array} \right]\)
• E) \(\left[ \begin{array} { c c }
• 1 & - 3 \\
• - 5 & 2
• \end{array} \right] \left[ \begin{array} { c }
• - 25 \\
• 34
• \end{array} \right] = \left[ \begin{array} { c }
• - 4 \\
• 7
• \end{array} \right]\)

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Definitions:

Correlation Coefficient

A statistical measure that indicates the extent to which two variables fluctuate together.

Independent Variable

A variable in an experiment that is manipulated to determine its effect on the dependent variable.

Dependent Variable

The variable in an experiment that is observed and measured to see how it is influenced by the independent variable.

Correlation Coefficient

A numerical measure that indicates the extent of a linear relationship between two variables, ranging from -1 to 1.