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

question 30

Multiple Choice

Determine whether {v₁, v₂, v₃} is a basis for R³
-Let $\mathrm { H } = \left\{ \left[ \begin{array} { c } \mathrm { a } + 3 \mathrm {~b} + 4 \mathrm {~d} \\ \mathrm { c } + \mathrm { d } \\ - 3 \mathrm { a } - 9 \mathrm {~b} + 4 \mathrm { c } - 8 \mathrm {~d} \\ - \mathrm { c } - \mathrm { d } \end{array} \right] : a , b , c , \mathrm {~d} \right.$ in $\left. \mathscr { R } \right\}$
Find the dimension of the subspace $\mathrm { H }$ .

• A) \(\operatorname { dim } \mathrm { H } = 2\)
• B) \(\operatorname { dim } \mathrm { H } = 4\)
• C) \(\operatorname { dim } \mathrm { H } = 3\)
• D) \(\operatorname { dim } \mathrm { H } = 1\)

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Definitions:

Conceptual

Pertaining to concepts or ideas; concerned with the theoretical, rather than practical aspects of something.

Stereotypy

The repetition of meaningless gestures or movements. One of the manifestations of a developmental disorder.

Neurodevelopmental Disorders

A group of conditions that emerge in childhood and are characterized by developmental deficits that produce impairments in personal, social, academic, or occupational functioning.

Non-functional Gestures

Gestures that do not serve a direct practical purpose or that do not convey meaningful communication in a given context.