1. The problem statement, all variables and given/known data let U be a 3x3 matrix containng columns C1, C2, C3. The three column vectors C1= (a,0,0) , C2=(b,d,0), C3=(c,e,f) prove that if a=0 or d=0 or f=0 (3cases), the columns of U are dependent? problem from Linear algebra and applications, fourth editon, Gilbert strang 2. Relevant equations no eqations 3. The attempt at a solution I successfully proved the first two cases if a=0, if we multiply C3 or C2 with zero then C1 will be equal to C2 or C3. The columns become independent if d=0, if we multiply C1 with b/a and C2 with a/b, C1 and C2 will be identical and the columns become independent. But i dont know how to prove the third case, i tried with different comibinations of scalars with multiply with C2 and C3, but i can't make this two columns identical. Enlighten me.