Use Inverses to Solve Matrix Equations
Write the Linear System $$9 x - 2 y = 51$$

question 72

Multiple Choice

Use Inverses to Solve Matrix Equations
Write the linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the
constant matrix.
- $$9 x - 2 y = 51$$
$$6 y = 36$$

• A) \(\left[ \begin{array} { r r } 9 & - 2 \\ 0 & 6 \end{array} \right] \left[ \begin{array} { l } x \\ y \end{array} \right] = \left[ \begin{array} { l } 51 \\ 36 \end{array} \right]\)
• B)
• \[\left[ \begin{array} { c c }
• 9 & - 2 \\
• 6 & 36
• \end{array} \right] \left[ \begin{array} { l }
• x \\
• y
• \end{array} \right] = \left[ \begin{array} { l }
• 51 \\
• 0
• \end{array} \right]\]
• C)
• \[\left[ \begin{array} { c c }
• 6 & 0 \\
• 9 & - 2
• \end{array} \right] \left[ \begin{array} { l }
• x \\
• y
• \end{array} \right] = \left[ \begin{array} { c }
• 36 \\
• - 2
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { r r }
• 51 & - 2 \\
• 36 & 0
• \end{array} \right] \left[ \begin{array} { l }
• x \\
• y
• \end{array} \right] = \left[ \begin{array} { l }
• 9 \\
• 6
• \end{array} \right]\]

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Definitions:

T Distribution

A type of probability distribution that is symmetric and bell-shaped but has heavier tails than the normal distribution, used especially in small sample analysis.

Degrees of Freedom

The count of distinct values or quantities that can change during an analysis while still adhering to all constraints.

Normal Distribution

This refers to a probability distribution characterized by its symmetry about the mean, highlighting that data closer to the mean are encountered more frequently than data far from the mean.

Degrees of Freedom

The number of independent pieces of information used in the calculation of a statistic, often representing the number of values free to vary.