Linear AlgebraChallengeRow Reduction & Rank

Row Reduction & Rank · Challenge problem

The system

2x + y + 3z = 24, \qquad x + y + z = 13, \qquad 3x + 2y + 4z = 37

has infinitely many solutions. How many of them have $x$ , $y$ and $z$ all nonnegative integers?