Answer
The second system also has a solution.
Work Step by Step
Let A be the coefficient matrix of the given system of equations.
x= $\begin{bmatrix}
x1\\
x2\\
x3
\end{bmatrix}$ is a solution of Ax = b, where b = $\begin{bmatrix}
0\\
1\\
9
\end{bmatrix}$
This means that b $\in$ Col A
Col A is a subspace of $R^3$
Therefore, Col A is closed under scalar multiplication.
$\begin{bmatrix}
0\\
5\\
45
\end{bmatrix}$ = 5b $\in$ Col A
This implies that the second system Ax = 5b, also has a solution.
