Write the System as a Vector Equation or Matrix Equation $$\begin{array} { l l } 2 x _ { 1 } + x _ { 2 } - 6 x _ { 3 } & = - 6 \\6 x _ { 1 } - 4 x _ { 2 } & = 2\end{array}$$

question 6

Multiple Choice

Write the system as a vector equation or matrix equation as indicated.
-Write the following system as a matrix equation involving the product of a matrix and a vector on the left side and a vector on the right side. $$\begin{array} { l l } 2 x _ { 1 } + x _ { 2 } - 6 x _ { 3 } & = - 6 \\6 x _ { 1 } - 4 x _ { 2 } & = 2\end{array}$$

• A) \(\left[ \begin{array} { r r r } 2 & 1 & - 6 \\ 6 & 4 & 1 \end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = \left[ \begin{array} { r } - 6 \\ 2 \end{array} \right]\)
• B) \(\left[ \begin{array} { r r r } 2 & 1 & - 6 \\ 6 & - 4 & 0 \end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \\ x _ { 3 } \end{array} \right] = \left[ \begin{array} { r } - 6 \\ 2 \end{array} \right]\)
• C) \(\left[ \begin{array} { r r } 2 & 6 \\ 1 & - 4 \\ - 6 & 0 \end{array} \right] \left[ \begin{array} { l } x _ { 1 } \\ x _ { 2 } \end{array} \right] = \left[ \begin{array} { r } - 6 \\ 2 \end{array} \right]\)
• D) \(\left[ \begin{array} { c c r } x _ { 1 } & x _ { 2 } & x _ { 3 } \\ 6 & - 4 & 0 \end{array} \right] \left[ \begin{array} { r } 2 \\ 1 \\ - 6 \end{array} \right] = \left[ \begin{array} { r } - 6 \\ 2 \end{array} \right]\)

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Definitions:

Heuristics

Mental shortcuts or rules of thumb that simplify decision making, but can sometimes lead to cognitive biases.

Mnemonic Devices

Techniques a person can use to help them improve their ability to remember something, often by associating it with something more familiar or patterning.

Cognitive Shortcuts

Heuristic methods or simple strategies used by the human mind to make decisions or solve problems quickly.

Heuristics

Mental shortcuts or rules of thumb that facilitate fast and efficient decision-making, although not always leading to the perfect solution.