Determine Whether {V1, V2, V3} Is a Basis For , And

question 46

Multiple Choice

Determine whether {v1, v2, v3} is a basis for
$\mathbf { b } _ { 1 } = \left[ \begin{array} { l } 1 \\ 1 \end{array} \right] , \mathbf { b } _ { 2 } = \left[ \begin{array} { r } 1 \\ - 1 \end{array} \right] , \mathbf { x } = \left[ \begin{array} { r } 3 \\ - 5 \end{array} \right]$ , and $B = \left\{ \mathbf { b } _ { 1 } , \mathbf { b } _ { 2 } \right\}$



- $\mathbf { b } _ { 1 } = \left[ \begin{array} { r } 3 \\ 2 \\ - 3 \end{array} \right] , \mathbf { b } _ { 2 } = \left[ \begin{array} { r } 5 \\ - 3 \\ - 1 \end{array} \right] , \mathbf { x } = \left[ \begin{array} { r } - 16 \\ 2 \\ 8 \end{array} \right]$ , and $B = \left\{ \mathbf { b } _ { 1 } , \mathbf { b } _ { 2 } \right\}$

• A) \(\left[ \begin{array} { l } - 2 \\ - 3 \end{array} \right]\)
• B) \(\left[ \begin{array} { r } - 128 \\ - 2 \\ - 32 \end{array} \right]\)
• C) \(\left[ \begin{array} { l } - 2 \\ - 2 \end{array} \right]\)
• D) \(\left[ \begin{array} { r } - 38 \\ - 38 \\ 46 \end{array} \right]\)

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Definitions:

Naturally Occurring

Events or phenomena that happen without human intervention or manipulation, often observed in research to understand natural behaviors or processes.

Intrinsic Case Study

A case study where the interest is in the case itself because of its unique or peculiar nature, rather than to generalize or compare.