Question

Match each determinant value to the correct matrix - partially solved, see photo

Answer 1

We would find the determinant of each matrix and match them with the given values.

`\begin{gathered} \begin{bmatrix}{1} & {5} & {-\text{ 2}} \\ {7} & {4} & {1} \\ {-\text{ 3}} & {1} & {6}\end{bmatrix} \\ Determinant\text{ = 1\lparen4}*6\text{ - 1}*1)\text{ - 5\lparen7 }*6-1*-3)-2(7*1-4*-3) \\ =\text{ \lparen24-1\rparen-5\lparen42+3\rparen-2\lparen7+12\rparen} \\ =\text{ 23-225-38} \\ =\text{ - 240} \end{gathered}`
`\begin{gathered} \begin{bmatrix}{7} & {2} & {5} \\ {2} & {-2} & {5} \\ {1} & {11} & {4}\end{bmatrix} \\ Determinant\text{ = 7\lparen-2}*4\text{ -5}*11)-2(2*4-5*1)+5(2*11-1*-2) \\ =7(-8-55)-2(8-5)+5(22+2) \\ =-441-6+120 \\ =\text{ - 327} \end{gathered}`
`\begin{gathered} \begin{bmatrix}{3} & {6} & {4} \\ {3} & {6} & {7} \\ {2} & {4} & {-2}\end{bmatrix} \\ Determinant\text{ = 3\lparen6}*-2\text{ - 7}*4)-6(3*-2-7*2)+4(3*4-6*2) \\ =3(-12-28)-6(-6-14)+4(12-12) \\ =-120+120+0 \\ =\text{ 0} \end{gathered}`
`\begin{gathered} \begin{bmatrix}{1} & {8} & {-4} \\ {2} & {3} & {3} \\ {-1} & {1} & {-4}\end{bmatrix} \\ Determinant\text{ = 1\lparen3}*-4-1*3)-8(2*-4-3*-1)-4(2*1-3*-1) \\ =\text{ 1\lparen-12-3\rparen-8\lparen-8+3\rparen-4\lparen2+3\rparen} \\ =-15+40-20 \\ =\text{ 5} \end{gathered}`