Given he following system determine conditions on a, b and c for which system will have a unique solution, an infinite number of solutions and no solutions

Question

anonymous · Answer

x+3y-4z=8
-x-y+z=-4
2x+z=4
ax+by+cz=0

anonymous · Answer

I have examples on this question but they all have each equation set to a or b or c

anonymous · Answer

not sure how to do this
I changed row 2 and three and set the first terms to zero but how do I make a 0??

anonymous · Answer

it would be a unique system if a and b and c were equal to zero, make sense? lol

anonymous · Answer

no solution if a and b and c did not equal zero

anonymous · Answer

try finding the determinant of the matrix|dw:1362511563261:dw| and set it not equal to zero.the condition obtained in terms of a,b,c will then be the condition for the system to have a unique finite solution