2000019001
Level:
B
Four matrices are given:
\[\]
$\left (\array{
1& -1& 0\cr
2& 0& 1\cr
1& 1& -1} \right ),$
$\left (\array{
1& -3& 0\cr
2& -5& 1\cr
1& 0& -1} \right ),$
$\left (\array{
-3& -1& 0\cr
-5& 0& 1\cr
0& 1& -1} \right ),$
$\left (\array{
1& -1& -3\cr
2& 0& -5\cr
1& 1& 0} \right )$
\[\]
We want to practice Cramer's rule for solving a system of linear equations. Which of the following systems can be solved using determinants of the four matrices given above?
\[\begin{aligned}
x- y = -3 & &
\\2x + z = -5 & &
\\x + y -z= 0 & &
\end{aligned}\]
\[\begin{aligned}
x- y-3z = 0 & &
\\2x - 5z = 1 & &
\\x + y = -1& &
\end{aligned}\]
\[\begin{aligned}
-3x- y = 0 & &
\\-5x + z = 1 & &
\\ y -z= -1& &
\end{aligned}\]
\[\begin{aligned}
x- y = 3 & &
\\2x + z = 5 & &
\\x + y -z= 0 & &
\end{aligned}\]
