EXPLANATION
Given the system of equations:
(1) x +2y = 5
(2) x -3y = 7
[tex]\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc[/tex][tex]=1\cdot \left(-3\right)-2\cdot \:1[/tex]Remove parentheses:
[tex]=-1\cdot \:3-2\cdot \:1[/tex][tex]\mathrm{Multiply\:the\:numbers:}\:1\cdot \:3=3[/tex][tex]=-3-2\cdot \:1[/tex][tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:1=2[/tex][tex]=-3-2[/tex][tex]\mathrm{Subtract\:the\:numbers:}\:-3-2=-5[/tex][tex]=-5[/tex]In conclusion, the determinant is -5
