# Thread: Two Liner Algebra Problems

1. ## Two Liner Algebra Problems

Hello

$(1-i)x-iy=0$
$2x+(1-i)y=0$

2.-Prove that the interchange of two rows of a matrix can be accomplished by a finite sequence of elementary row operations of the other two types.

Thanks a lot

2. 1. Note that $2=(1+i)(1-i)=-i(1+i)^2$.

2. Suppose you want to interchange $R_1=x$ and $R_2=y$.

First add $R_2$ to $R_1$ to get $R_1=x+y$.

Next subtract $R_1$ from $R_2$ to get $R_1=x+y$, $R_2=-x$.

Next add $R_2$ to $R_1$ to get $R_1=y$, $R_2=-x$. Finally multiply $R_2$ by $-1$ (interchanging two rows or columns changes the sign of the determinant).