Exam 11: Determinants

Find the value of the second-order determinant: $\left|\begin{array}{ll}\frac{2}{5} & \frac{-1}{4} \\ \frac{4}{5} & \frac{3}{4}\end{array}\right|$

Evaluate the determinant: $\left|\begin{array}{ccccc}2 & -1 & 3 & 2 & 5 \\ 5 & 3 & 6 & -4 & 1 \\ 3 & 0 & 6 & 2 & 4 \\ 1 & 4 & 4 & 5 & 2 \\ 2 & 4 & -1 & 3 & 6\end{array}\right|$

Solve by determinants: $-2 y-6=5 x$ $2 y+2 x-9=0$

Find the value of the second-order determinant: $\left|\begin{array}{cc}-2 & 1 \\ 7 & -2\end{array}\right|$

Evaluate the determinant: $\left|\begin{array}{lll}4 & 1 & 3 \\ 1 & 2 & 0 \\ 6 & 4 & 1\end{array}\right|$

Solve by determinants: $3 x+2 y-5 z+w=2$ x-2y+z-w=2 x+y+z+2w=2 x-y-z-3w=-1

Solve by determinants: $2 x+5 y-3 z-4 w=20$ 7x-3y+z-2w =5 x-3y-z-w =-10 x+3y+4z+5w =3

Evaluate the determinant: $\left|\begin{array}{ccc}-1 & 2 & -4 \\ 1 & -5 & 6 \\ 3 & 0 & 7\end{array}\right|$

Find the value of the second-order determinant: $\left|\begin{array}{ll}4 & 4 \\ 4 & 4\end{array}\right|$

Solve by determinants: $11 x-5 y=3$ $2 x+6 y=4$

Solve by determinants: $3 x+2 y=4$ $x-2 y=2$

Find the value of the second-order determinant: $\left|\begin{array}{cc}5 & -10 \\ 1 & -2\end{array}\right|$

Solve by determinants: $2 x+y-2 z+w=-14$ x-2y+z=-2 3x+y-2w=-8 3y+3z-w=25

Evaluate the determinant: $\left|\begin{array}{ccc}0.3 & 1.2 & -0.5 \\ 0.4 & -1.4 & 1.3 \\ -0.2 & 1.3 & 2.2\end{array}\right|$

Solve by determinants: $3 x+3 z=6$ 4y+2z =-12 2x+6y+4z =9 2x+4y+4w =-8