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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


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    Note that "D" could never be an answer for this type of question.2012-02-09

0 Answers 0