Write the System as a Vector Equation or Matrix Equation $$\begin{array} { l } 6 x _ { 1 } - 6 x _ { 2 } - x _ { 3 } = 5 \\6 x _ { 1 } + 3 x _ { 3 } = - 5\end{array}$$

question 62

Multiple Choice

Write the system as a vector equation or matrix equation as indicated.
-Write the following system as a vector equation involving a linear combination of vectors. $$\begin{array} { l } 6 x _ { 1 } - 6 x _ { 2 } - x _ { 3 } = 5 \\6 x _ { 1 } + 3 x _ { 3 } = - 5\end{array}$$

• A) \(x _ { 1 } \left[ \begin{array} { l } 6 \\ 6 \end{array} \right] + x _ { 2 } \left[ \begin{array} { r } - 6 \\ 0 \end{array} \right] + x _ { 3 } \left[ \begin{array} { c } - 1 \\ 3 \end{array} \right] = \left[ \begin{array} { r } 5 \\ - 5 \end{array} \right]\)
• B) \(x _ { 1 } \left[ \begin{array} { c } 6 \\ 6 \\ - 1 \end{array} \right] + x _ { 2 } \left[ \begin{array} { c } 6 \\ 0 \\ 3 \end{array} \right] = \left[ \begin{array} { c } 5 \\ - 5 \\ 0 \end{array} \right]\)
• C) \(6 \left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] - 6 \left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] - \left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = \left[ \begin{array} { r } 5 \\ - 5 \\ 0 \end{array} \right]\)
• D) \(x _ { 1 } \left[ \begin{array} { l } 6 \\ 6 \end{array} \right] + x _ { 2 } \left[ \begin{array} { r } - 6 \\ 1 \end{array} \right] + x _ { 3 } \left[ \begin{array} { c } 1 \\ 3 \end{array} \right] = \left[ \begin{array} { r } 5 \\ - 5 \end{array} \right]\)

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Definitions:

Testable Prediction

A statement or hypothesis that can be verified or falsified through experimental or observational means.

Naturalistic Observation

An examination method where people are observed in their natural settings without any alterations made by the researcher.

Theory

A systematic explanation of an aspect of the natural world, grounded in observation, experimentation, and reasoning.

Observations

The active acquisition of information from a primary source, using the senses or tools and instruments for measuring and recording.