## Elementary Linear Algebra 7th Edition

(a) A basis for the row space is given by $$S=\{(1,-3,2),(0,14,7)\}.$$ (b) The rank of the matrix is $2$.
Let $A$ be given by $$A=\left[\begin{array}{rrr}{1} & {-3} & {2} \\ {4} & {2} & {1}\end{array}\right]$$ The reduced form of $A$ is given by $$\left[ \begin {array}{ccc} 1&-3&2\\ 0&14&-7 \end {array} \right]$$ (a) A basis for the row space is given by $$S=\{(1,-3,2),(0,14,7)\}.$$ (b) The rank of the matrix is $2$.