Question

Find the conditions on a, b, and c so that the following linear system of equations have a solution.

x + 2y − 3z = a

2x + 6y − 11z = b

2x − 4y + 14z = 2c

Answer 1

$\Delta=1\cdot(42-22)-2\cdot(14+11)-3\cdot(-4-6)=20-50+30=0,$

there are no solutions for any a, b, c.