Question

how do i check if the solution set is a subspace?

Answer 1

\[\left[\begin{matrix}x_{1} \\ x_{2} \\ x_{3} \end{matrix}\right] = t \left(\begin{matrix}1 \\ -3 \\ 1\end{matrix}\right)+\left[\begin{matrix}2 \\ -2 \\ 0\end{matrix}\right]\]

Answer 2

first, what exactly is the solution set here? Also how do i check if its a subspace? That is the solution to a matrix eqation: \[\left[\begin{matrix}1 & 1 & 2 \\ 2 & 1 & 1\\ 3 & 2 & 3 \end{matrix}\right]x = \left[\begin{matrix}0\\ 2 \\ 2\end{matrix}\right]\]

Answer 3

The above cannot be the basis of a subspace because it must satisfy the following conditions:
1. The zero vector is contained in the above set for some value of t.
2. satisfy scalar multiplication requirement, a(v) + b(v) = (a+b)v.