given matrix A= (1 -1 1 -1
2 -2 2 -2
1 -2 0 -1
4 2 1 0)
prove that the determinant det A=0 without calculating the determinant.

Question

given  matrix A= (1  -1  1  -1
                              2  -2  2  -2
                              1  -2  0  -1
                              4   2   1   0)
prove that the determinant det A=0 without calculating the determinant.

amistre64 · Answer

if one row or column is a scalar of another, I believe the det goes to 0

anonymous · Answer

R2=2R1

amistre64 · Answer

R2 = R1*2

amistre64 · Answer

yeah, what Gowt said :)

anonymous · Answer

do  you think that this should be a sufficient answer? 
if R2= 2R1, det=0
(2  -2  2  -2)= 2( 1  -1  1  -1)
                     =   (2  -2  2  -2)

amistre64 · Answer

hmmm, that seems more "teacher" dependant.  If you have literature where you can cite the thrm used ... that might be a better route to take

amistre64 · Answer

it has to do with linear depence/independence ....