Determine if the vector u is in the column space of matrix A and whether it is in the null space of A.
-$$\mathbf { v } _ { 1 } = \left[ \begin{array} { r }
1 \
- 3 \
3
\end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { r }
- 3 \
8 \
8
\end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { r }
2 \
- 2 \
- 7
\end{array} \right]$$
A) Yes
B) No

Question

Determine if the vector u is in the column space of matrix A and whether it is in the null space of A.
-$$\mathbf { v } _ { 1 } = \left[ \begin{array} { r } 
1 \
- 3 \
3
\end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { r } 
- 3 \
8 \
8
\end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { r } 
2 \
- 2 \
- 7
\end{array} \right]$$
A) Yes
B) No

Quizplus · Accepted Answer

BThe question asks if a vector $ \mathbf{u} $ is in the column space and null space of matrix $ \mathbf{A} $, but the vector $ \mathbf{u} $ is not provided in the question. Without knowing what $ \mathbf{u} $ is, we cannot determine if it is in the column space or the null space of $ \mathbf{A} $, where $ \mathbf{A} $ is presumably formed by the vectors $ \mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3 $ as its columns. Therefore, without specific information about $ \mathbf{u} $, no determination can be made.

Determine If the Vector U Is in the Column Space