Cramer's rule/2x2/1/Example
< Cramer's rule < 2x2 < 1
We solve the
linear system
(
4
3
−
1
5
)
(
x
1
x
2
)
=
(
2
7
)
{\displaystyle {}{\begin{pmatrix}4&3\\-1&5\end{pmatrix}}{\begin{pmatrix}x_{1}\\x_{2}\end{pmatrix}}={\begin{pmatrix}2\\7\end{pmatrix}}\,}
using
Cramer's rule
. This yields
x
1
=
det
(
2
3
7
5
)
det
(
4
3
−
1
5
)
=
−
11
23
{\displaystyle {}x_{1}={\frac {\det {\begin{pmatrix}2&3\\7&5\end{pmatrix}}}{\det {\begin{pmatrix}4&3\\-1&5\end{pmatrix}}}}=-{\frac {11}{23}}\,}
and
x
2
=
det
(
4
2
−
1
7
)
det
(
4
3
−
1
5
)
=
30
23
.
{\displaystyle {}x_{2}={\frac {\det {\begin{pmatrix}4&2\\-1&7\end{pmatrix}}}{\det {\begin{pmatrix}4&3\\-1&5\end{pmatrix}}}}={\frac {30}{23}}\,.}
