Which values of K make the matrix inconsistent?

Question

anonymous · Answer

-6	k	0	
-2	-2	-2
-1	-1	0

anonymous · Answer

Answer: when k is any real number. lolz

watchmath · Answer

it is inconsistent if the first row is a multiple of the second or the third row. From the last entry (the 0 and -2 ), the first row can't be a multiple of the second row.

watchmath · Answer

sorry I made a mistake above

watchmath · Answer

Is this a homogenous equation AX=0 or AX=b. In the second case what is our b here?

anonymous · Answer

It's augmented. :)

anonymous · Answer

Ax=b
All values of k make the matrix inconsistent because the last row has a 'b' value of 0. The first two cannot equal zero. Am I correct?

watchmath · Answer

sok, so to make it inconsistent then k=-6. Because we will have -6x-6y=0. If we divide that by -3 we have -2x-2y=0. Meanwhile the second row tells us that -2x-2y=2 (and it can't be 0 and 2 at the same time)

anonymous · Answer

no that makes it consistent?

watchmath · Answer

It has no solution, so it is inconsistent

anonymous · Answer

right. but it has no solution no mater the case for k.

watchmath · Answer

Ah you are right! :D

anonymous · Answer

:) Silly matrices