Solve the Problem , And $\mathbf { b } = \left[ \begin{array} { r } 2 \\ - 10 \\ 6 \end{array} \right]$

question 2

Multiple Choice

Solve the problem.
-Let $\mathbf { a } _ { 1 } = \left[ \begin{array} { r } 3 \\ 4 \\ - 4 \end{array} \right] , \mathbf { a } _ { 2 } = \left[ \begin{array} { r } - 4 \\ 1 \\ 1 \end{array} \right]$ , and $\mathbf { b } = \left[ \begin{array} { r } 2 \\ - 10 \\ 6 \end{array} \right]$
Determine whether $\mathbf { b }$ can be written as a linear combination of $\mathbf { a } _ { \mathbf { 1 } }$ and $\mathbf { a } _ { \mathbf { 2 } }$ . In other words, determine whether weights $x _ { 1 }$ and $x _ { 2 }$ exist, such that $x _ { 1 } a _ { 1 } + x _ { 2 } a _ { 2 } = b$ . Determine the weights $x _ { 1 }$ and $x _ { 2 }$ if possible.

• A) No solution
• B) \(x _ { 1 } = - 1 , x _ { 2 } = - 3\)
• C) \(x _ { 1 } = - 2 , x _ { 2 } = - 2\)
• D) \(x _ { 1 } = - 2 , x _ { 2 } = - 1\)

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Definitions:

Uncontrolled Anger

Intense feelings of anger that are difficult to manage or control, often leading to aggressive behavior or confrontation.

Hallucinations

Perceptual experiences that are not real.

Violent Behavior

Actions that involve physical force intended to hurt, damage, or kill someone or something.

Substance Use

The consumption of drugs or alcohol, potentially leading to substance abuse or dependence.