We would find the determinant of each matrix and match them with the given values.
[tex]\begin{gathered} \begin{bmatrix}{1} & {5} & {-\text{ 2}} \\ {7} & {4} & {1} \\ {-\text{ 3}} & {1} & {6}\end{bmatrix} \\ Determinant\text{ = 1\lparen4}\times6\text{ - 1}\times1)\text{ - 5\lparen7 }\times6-1\times-3)-2(7\times1-4\times-3) \\ =\text{ \lparen24-1\rparen-5\lparen42+3\rparen-2\lparen7+12\rparen} \\ =\text{ 23-225-38} \\ =\text{ - 240} \end{gathered}[/tex][tex]\begin{gathered} \begin{bmatrix}{7} & {2} & {5} \\ {2} & {-2} & {5} \\ {1} & {11} & {4}\end{bmatrix} \\ Determinant\text{ = 7\lparen-2}\times4\text{ -5}\times11)-2(2\times4-5\times1)+5(2\times11-1\times-2) \\ =7(-8-55)-2(8-5)+5(22+2) \\ =-441-6+120 \\ =\text{ - 327} \end{gathered}[/tex][tex]\begin{gathered} \begin{bmatrix}{3} & {6} & {4} \\ {3} & {6} & {7} \\ {2} & {4} & {-2}\end{bmatrix} \\ Determinant\text{ = 3\lparen6}\times-2\text{ - 7}\times4)-6(3\times-2-7\times2)+4(3\times4-6\times2) \\ =3(-12-28)-6(-6-14)+4(12-12) \\ =-120+120+0 \\ =\text{ 0} \end{gathered}[/tex][tex]\begin{gathered} \begin{bmatrix}{1} & {8} & {-4} \\ {2} & {3} & {3} \\ {-1} & {1} & {-4}\end{bmatrix} \\ Determinant\text{ = 1\lparen3}\times-4-1\times3)-8(2\times-4-3\times-1)-4(2\times1-3\times-1) \\ =\text{ 1\lparen-12-3\rparen-8\lparen-8+3\rparen-4\lparen2+3\rparen} \\ =-15+40-20 \\ =\text{ 5} \end{gathered}[/tex]
