Determine Whether {V₁, V₂, V₃} Is a Basis for R³

question 20

Multiple Choice

Determine whether {v₁, v₂, v₃} is a basis for R³
- $$\mathbf { v } _ { 1 } = \left[ \begin{array} { r } - 2 \\4 \\- 8\end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { l } 1 \\0 \\3\end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { r } 4 \\- 4 \\14\end{array} \right]$$

• A) Yes
• B) No

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Definitions:

Silicon

A chemical element with symbol Si and atomic number 14, known for its semiconductor properties in electronics.

Metals

Elements that are typically hard, shiny, malleable, fusible, and ductile, with good electrical and thermal conductivity.

Iron

A durable and abundant metallic element, symbol Fe, atomic number 26, used extensively as a component in steel and various other alloys.

Lead

A heavy metal element with the symbol Pb and atomic number 82, known for its density, malleability, and resistance to corrosion.