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Question 2 and 3

1. The problem statement, all variables and given/known data

For what values of c does the system have no solutions? I figured out the other ones, for c=0 we can assign a parameter to x_{1}and it will then have infinite solutions. For c=1 the system will have a unique solution. I know that if the matrix is in reduced row echelon form, and if the last row is all zeroes except for the right hand side of the equality, it has no solutions, but how can I manipulate the augmented matrix to make it so?

2. Relevant equations

Here is the augmented matrix:

1 1 3|c

c 1 5|4

1 c 4|c

3. The attempt at a solution

I can use elementary row/column operations, but I end up with this matrix in trying to make the bottom row 0...

1 1 3 |c

0 (1-c) (5-3c) |-c^{2}+4

0 (c-1) 1 |-c^{2}

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# Systems of Linear Equations

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