How many solutions does each system have
- A. Unique solution
- B. No solutions
- C. Infintely many solutions
- D. None of the above.
$\left(\begin{array}{cc|r} 1 & 0 & 6\\ 0 & 1 & -4\\ \end{array}\right)$
My answer: A - Unique solution
x = 6, y= -4
$\left(\begin{array}{cc|r} 1 & 0 & 8\\ 0 & 1 & -11\\ 0 & 0 & 0 \end{array}\right)$
My answer: A - Unique solution
x = 8, y= -11 Although, I think I recall hearing that if the bottom row is all zeroes, has infintely many solutions?
$\left(\begin{array}{ccc|r} 1 & 0 & 14 & 0\\ 0 & 1 & 15 & 0\\ 0 & 0 & 0 & 1\\ \end{array}\right)$
My answer: B - No solutions
As the bottom row is invalid. Or am I allowed to 'overlook that'? And say it has infinitely many solutions?
$\left(\begin{array}{ccc|r} 0 & 1 & 0 & -4\\ 0 & 0 & 1 & 2\\ \end{array}\right)$
My answer: A - Unique solution y = -4, z = 2