Exam 11: Determinants

Solve by determinants: $2.5 x+13.2 y+4.2 z=4.4$ 3.2x+2.5y-2.2z=-2.7 1.5x-2.4y-3.5z=-5.1

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

Find the value of the second-order determinant: $\left|\begin{array}{cc}3 & \frac{1}{5} \\ \frac{-10}{3} & \frac{2}{9}\end{array}\right|$

Solve for $x$ and $y$ by determinants: $(a+2) x+(a-3) y=5$ $(a-4) x+(a+6) y=5$

Find the value of the second-order determinant: $\left|\begin{array}{cc}5 & x^{2}-36 \\ 1 & (x-6)^{2}\end{array}\right|$

Kirchhoff's rules were applied to a three-loop network. Solve for currents $l_{1}, l_{2}$ , and $l_{3}$ in this resulting system of equations: $76.0 I_{1}-25.0 I_{2}-50.0 I_{3}=10.0$ $-25.0 l_{1}+56.0 I_{2}-1.00 I_{3}=0.00$ $-50.0 l_{1}-1.0 I_{2}+106 l_{3}=0.00$

Determine the coefficients $a, b$ , and $c$ which balance the chemical equation $a \mathrm{C}_{4} \mathrm{H}_{10}+13 \mathrm{O}_{2} \rightarrow b \mathrm{H}_{2} \mathrm{O}+$ $c \mathrm{CO}_{2}$ . In other words, solve this system: C: $\quad 4 a=0 b+c$ $\mathrm{H}: \quad 10 a=2 b+0 c$ O: $\quad 26=b+2 c$

Solve by determinants: $3 x+2 y=6$ 3y-4z=7 2x+3z=7

Find the value of the second-order determinant: $\left|\begin{array}{cc}-x^{2}+5 x & x \\ 6 & -2\end{array}\right|$

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

Solve by determinants: $2 x+2 y-3 z=11$ 3y+2z+w=10 3x-4y+2w=-4 z+3w-v=14 3y+2w=23

Solve by determinants: $3 x-4 y=-22$ $5 x+3 y=60$

Evaluate the determinant: $\left|\begin{array}{ccc}1.0 & 8.8 & -3.1 \\ 7.8 & 1.5 & 5.3 \\ -3.3 & 2.0 & 6.4\end{array}\right|$

Find the value of the second-order determinant: $\left|\begin{array}{cc}\frac{1}{5} & \frac{3}{5} \\ \frac{-6}{30} & \frac{9}{15}\end{array}\right|$

Solve by determinants: $x+2 y-2 z=54$ 3x-y+4z=-26 2x+3y+z=49

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

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

Solve by determinants: $x+2 y+z+w=2$ x+3y+2z+w =0 2x-y+2z-3w =-1 x+y-4z-w =-14

Solve by determinants: $\frac{12}{x}+\frac{3}{y}=4$ $\frac{20}{x}-\frac{9}{y}=2$

Solve by determinants: $7 x+13 y-7 z=24$ $4 x-6 y+10 z=37$ $6 x-26 y+33 z=15$