The question is to reduce the matrix as close to row-echelonform as you can. Onc

Question

The question is to reduce the matrix as close to row-echelonform as you can. Once you have the solution, find all possiblevalues of p & q such that the system has: i) a unique solution ii) infinitely many solutions iii) no solutions 1 1 0 | 1 0 1 1 | -2 2 0 p | q       I have reduced this to 1 0 0 | (-1-q) / (2-p) 0 1 0 | (2+q) / (2-p) 0 0 1 | (-4-q) / (2-p) I'm pretty sure this is the correct RREF, but I am not surehow to get all values of p & q so that they satisfy i) ii) andiii) The question is to reduce the matrix as close to row-echelonform as you can. Once you have the solution, find all possiblevalues of p & q such that the system has: i) a unique solution ii) infinitely many solutions iii) no solutions 1 1 0 | 1 0 1 1 | -2 2 0 p | q       I have reduced this to 1 0 0 | (-1-q) / (2-p) 0 1 0 | (2+q) / (2-p) 0 0 1 | (-4-q) / (2-p) I'm pretty sure this is the correct RREF, but I am not surehow to get all values of p & q so that they satisfy i) ii) andiii)

Explanation / Answer

You don't have to actually reduce it to RREF because it doesn'ttell you to and it's easier if it isnt. 1 1 0 | 1 0 1 1 | -2 0 0 p+2 | q - 6 This would be sufficient to do the question. i) This would have a unique solution if p + 2 is not equal to 0    so p + 2 != 0        p != -2    Unique solution if p != -2 ii) This system would have infinite solution if p + 2 = 0 and q - 6= 0     so p + 2 = 0    q - 6 = 0         p =-2         q = 6     Infinite solution if p = -2 q = 6 iii) This system would have no solution if p + 2 = 0 and q - 6 !=0    p = -2 q != 6    No solution if p = -2, q != 6 Hope this helps.

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