## Elementary Linear Algebra 7th Edition

(a) A basis for the solution space is \left[\begin{aligned}0\\0 \\0 \end{aligned}\right]. (b) The dimension of the solution space is $0$.
The coefficient matrix is given by $$\left[ \begin {array}{ccc} 4&-1&2\\ 2&3&-1 \\ 3&1&1\end {array} \right] .$$ The reduced row echelon form is $$\left[ \begin {array}{ccc} 1&0&0\\ 0&1&0 \\ 0&0&1\end {array} \right] .$$ The corresponding system is \begin{aligned} x &=0\\ y &=0\\ z&=0 \end{aligned}. The solution of the above system is $x=0$,$y=0$, $z=0$. This means that the solution space of $Ax = 0$ consists of the zero vector x= \left[\begin{aligned} x\\ y\\z \end{aligned}\right]= \left[\begin{aligned}0\\0 \\0 \end{aligned}\right] . (a) A basis for the solution space is \left[\begin{aligned}0\\0 \\0 \end{aligned}\right]. (b) The dimension of the solution space is $0$.