Determine whether b is in the column space of A.
-$$A = \left[ \begin{array} { r r c }
- 1 & 0 & 2 \
5 & 8 & - 10 \
- 3 & - 3 & 6
\end{array} \right] , \mathbf { b } = \left[ \begin{array} { r }
- 4 \
3 \
4
\end{array} \right]$$
A) Yes
B) No

Question

Determine whether b is in the column space of A.
-$$A = \left[ \begin{array} { r r c } 
- 1 & 0 & 2 \
5 & 8 & - 10 \
- 3 & - 3 & 6
\end{array} \right] , \mathbf { b } = \left[ \begin{array} { r } 
- 4 \
3 \
4
\end{array} \right]$$
A) Yes
B) No

Quizplus · Accepted Answer

To determine if b is in the column space of A, we need to check if the system Ax = b has a solution. The augmented matrix is $\left[ \begin{array} { r r c | r } - 1 & 0 & 2 & -4 \5 & 8 & -10 & 3 \- 3 & - 3 & 6 & 4\end{array} \right]$. Row reducing this matrix shows that the system is inconsistent, indicating that b is not in the column space of A.

Determine Whether B Is in the Column Space of A