Determine Whether the Vector U Belongs to the Null Space $h$

question 8

Multiple Choice

Determine whether the vector u belongs to the null space of the matrix A.
-Find all values of $h$ such that $\mathbf { y }$ will be in the subspace of $\mathfrak { R } ^ { 3 }$ spanned by $\mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 }$ if $\mathbf { v } _ { 1 } = \left[ \begin{array} { r } 1 \\ 2 \\ - 4 \end{array} \right]$ , $\mathbf { v } _ { 2 } = \left[ \begin{array} { r } 3 \\ 4 \\ - 8 \end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { r } - 1 \\ 0 \\ 0 \end{array} \right]$ , and $\mathbf { y } = \left[ \begin{array} { l } 4 \\ 2 \\ \mathrm {~h} \end{array} \right]$ .

• A) \(h = - 4\)
• B) all \(h \neq - 4\)
• C) \(h = - 16\)
• D) \(h = - 4\) or 0

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