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) \(x _ { 1 } = - 2 , x _ { 2 } = - 1\)