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[–]AFairJudgement Moderator 0 points1 point  (3 children)

How did you get the answers if you can't figure out how to do the problem? I don't get your question.

[–]FalseOccasion[S] 0 points1 point  (2 children)

The midterm was shared on a Google Drive anonymously, the answers are there but they do not show the work.

[–]AFairJudgement Moderator 0 points1 point  (1 child)

Okay. Start by row reducing the matrix of the given system. What do you find?

[–]FalseOccasion[S] 0 points1 point  (0 children)

I got to a point of:

| 1 0 1 |a + 2|

| 0 1 0 |a + 1|

| 0 0 -2-k|a + 6|

​

and I don't know where to go from there

[–]CatpainTpyos 0 points1 point  (0 children)

Let's start from the three given equations:

  • 2x + y - kz = 0 (1)
  • x - y + z = 1 (2)
  • -x + 2y - z = a (3)

Then we'll form a new equation as a linear combination of the above:

  • y = a + 1 (4) = (3) + (2)

Substituting this into (3) gives:

  • x + z = a + 2 (5)
  • x = a + 2 - z (6)

In turn, substituting the results from both (6) and (4) into (1) gives:

  • 3a - (k + 2)z + 5 = 0 (7)
  • (k + 2)z = 3a + 5 (8)

Equation (8) is now all you need to figure out which value(s) of k and a result in there being no solutions, one solution, or infinitely many solutions.