systems of equations: value of A that gives no solution to system

[2blue42]

Find the value of A if the following system has no solution:
x + y + z = 5
2x - y + 3z = 5
3x - y + Az = 7

 

[stapel]

Find the value of A if the following system has no solution:
x + y + z = 5
2x - y + 3z = 5
3x - y + Az = 7

You know, from experience, that a last row (in reduced-row echelon form) of "(all zeroes) equal to (something non-zero)" means that the system has no solution. What did you find when you did row operations to convert this to reduced-row echelon form?

Please show all of your steps. Thank you!

 

[pka]

Find the value of A if the following system has no solution:
x + y + z = 5
2x - y + 3z = 5
3x - y + Az = 7

If you understand determinants, here is another way,

In any case, do show your work.