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(Solved): restrictions on vectors in R^3 define subsets which are subspaces of R3can you explain the whole pro ...
restrictions on vectors in R^3 define subsets which are subspaces of R3
can you explain the whole process. what are the steps that lead to the answers?
![1. Do the given restrictions on vectors
\[
\left[\begin{array}{l}
x_{1} \\
x_{2} \\
x_{3}
\end{array}\right]
\]
in \( R^{3} \](https://media.cheggcdn.com/study/f14/f1412e5f-da63-4877-8308-4e116161828d/image)
1. Do the given restrictions on vectors \[ \left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right] \] in \( R^{3} \) define subsets which are subspaces of \( R^{3} \) ? a. \( x_{1}=x_{2} x_{3} \) answer: no b. \( x_{1}-x_{2}+x_{3}=2 \) answer: no c. \( x_{1}+x_{2}+x_{3}=0 \) or \( x_{1}-x_{2}+x_{3}=0 \) answer: no d. \( x_{1}+x_{2}+x_{3}=0 \) and \( x_{1}-x_{2}+x_{3}=0 \) answer: yes