## Elementary Linear Algebra 7th Edition

(a) A basis for the row space is, $$S=\left\{(1,0),(0,1)\right\}.$$ (b) The rank of the matrix is $2$.
Given the matrix $$\left[ \begin {array}{cc} 1&2\\ -4&3 \\ 6&1\end {array} \right] .$$ The reduced row echelon form is given by $$\left[ \begin {array}{cc} 1&0\\ 0&1 \\ 0&0\end {array} \right] .$$ (a) A basis for the row space is, $$S=\left\{(1,0),(0,1)\right\}.$$ (b) The rank of the matrix is $2$.