Question 1

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

Accepted Answer

27

Question 2

Kirchhoff's rules were applied to a four-loop network. Solve for currents $I_{1}, I_{2}, l_{3}$, and $I_{4}$ in this resulting system of equations:
$-2 I_{1}+3 I_{2}+2 I_{3}=-18$
$\begin{aligned}
3 I_{1}+3 I_{3}-4 I_{4} & =-13 \
I_{1}+5 I_{2}+5 I_{4} & =0 \
-10 I_{1}+I_{2}-5 I_{3}-8 I_{4} & =5
\end{aligned}$
Find the loop currents.

Accepted Answer

$I_{1}=2.0, I_{2}=-0.8, I_{3}=-5.8, I_{4}=0.4$

Question 3

Solve by determinants: $x-2 y+z=3$
$\begin{array}{r}
2 x+2 y-3 z=9 \
2 x-3 y+z=-9
\end{array}$

Accepted Answer

$x=66, y=78, z=93$

Question 4

Solve by determinants: $2 x-y=1$
$\begin{aligned}
& 4 y-z=3 \
& x-3 z=-2
\end{aligned}$

Accepted Answer

The answer of Solve by determinants: $2 x-y=1$
\(\begin{aligned}
& 4 y-z=3...

Question 5

A shipment of 10 calculators and 8 flash drives cost $\$ 246$. Another shipment of 4 calculators and 10 flash drives cost $\$ 180$. What does each item cost?

Accepted Answer

calculator

Question 6

Solve by determinants: $x+6 y=13$
$4 x-3 y=-29$

Accepted Answer

The answer of Solve by determinants: $x+6 y=13$
$4 x-3 y=-29$...

Question 7

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

Accepted Answer

The answer of Find the value of the second-order determinant:...

Question 8

Solve by determinants: $1.02 x-2.03 y=9.16$
$\begin{aligned}
& -2.05 x+3.04 z=-4.17 \
& -1.04 y-2.05 z=-2.02
\end{aligned}$

Accepted Answer

The answer of Solve by determinants: $1.02 x-2.03 y=9.16$
\(\begin{aligned}
& -2.05...

Question 9

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

Accepted Answer

The answer of Evaluate the determinant: \(\left|\begin{array}{ccc}3 & -2 &...

Question 10

Solve by determinants: $2 x-4 y=6$
$5 x-y=9$

Accepted Answer

The answer of Solve by determinants: $2 x-4 y=6$
$5 x-y=9$...

Question 11

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

Accepted Answer

The answer of Evaluate the determinant: \(\left|\begin{array}{cccc}3 & 1 &...

Question 12

Solve by determinants: $3 x-5 y+14 z=-55$
$\begin{aligned}
10 x+2 y-7 z & =43 \
2 x-y+z & =-10
\end{aligned}$

Accepted Answer

The answer of Solve by determinants: $3 x-5 y+14 z=-55$
\(\begin{aligned}
10...

Question 13

Evaluate the determinant: $\left|\begin{array}{cccc}0 & 5 & 2 & 4 \ 0 & 1 & 2 & -8 \ 4 & 0 & 12 & 2 \ 7 & 1 & 1 & 1\end{array}\right|$

Accepted Answer

The answer of Evaluate the determinant: \(\left|\begin{array}{cccc}0 & 5 &...

Question 14

Solve by determinants: $\frac{1}{x}+\frac{1}{y}-\frac{1}{z}=-2$
$\begin{aligned}
& \frac{2}{x}-\frac{3}{y}+\frac{2}{z}=13 \
& \frac{1}{x}+\frac{2}{y}+\frac{3}{z}=9
\end{aligned}$

Accepted Answer

The answer of Solve by determinants: $\frac{1}{x}+\frac{1}{y}-\frac{1}{z}=-2$
$\begin{aligned}
& \frac{2}{x}-\frac{3}{y}+\frac{2}{z}=13 \
& \frac{1}{x}+\frac{2}{y}+\frac{3}{z}=9
\end{aligned}$...

Question 15

Find the value of the second-order determinant: $\left|\begin{array}{cc}3 a & 5 \ 2 a & -6\end{array}\right|$

Accepted Answer

The answer of Find the value of the second-order determinant:...

Question 16

Solve by determinants: $2 x=3 y+18$
$y=5-3 x$

Accepted Answer

The answer of Solve by determinants: $2 x=3 y+18$
$y=5-3 x$...

Question 17

Solve by determinants: $x+y-2 z=14$
$\begin{aligned}
2 x-y+3 z & =-10 \
2 x+3 y-2 z & =8
\end{aligned}$

Accepted Answer

The answer of Solve by determinants: $x+y-2 z=14$
\(\begin{aligned}
2 x-y+3 z...

Question 18

Solve by determinants: $2 x+4 y=16$
$3 x-2 y=-8$

Accepted Answer

The answer of Solve by determinants: $2 x+4 y=16$
\(3 x-2...

Question 19

Kirchhoff's rules were applied to a four-loop network. Solve for currents $I_{1}, l_{2}, l_{3}$, and $I_{4}$ in this resulting system of equations:
$-6.0 I_{1}+2.0 I_{2}+4.0 I_{4}=-12$
$4.0 I_{1}+4.0 I_{2}-14 I_{4}=0$
$2.0 I_{1}-8.0 I_{2}+20 I_{3}+4.0 I_{4}=0$
$2.0 I_{2}-2.0 I_{3}=12$

Accepted Answer

The answer of Kirchhoff's rules were applied to a four-loop...

Question 20

Solve by determinants: $x+y+z=6$
$\begin{aligned}
-x+y & =-8 \
x-z & =1
\end{aligned}$

Accepted Answer

The answer of Solve by determinants: $x+y+z=6$
\(\begin{aligned}
-x+y & =-8 \
x-z...

Exam 11: Determinants

Evaluate the determinant: ∣3−11−1244−25∣\left|\begin{array}{ccc}3 & -1 & 1 \\ -1 & 2 & 4 \\ 4 & -2 & 5\end{array}\right|​3−14​−12−2​145​​

Solve by determinants: x−2y+z=3x-2 y+z=3x−2y+z=3 2x+2y-3z=9 2x-3y+z=-9

Solve by determinants: 2x−y=12 x-y=12x−y=1 4y-z=3 x-3z=-2

A shipment of 10 calculators and 8 flash drives cost $246\$ 246$246 . Another shipment of 4 calculators and 10 flash drives cost $180\$ 180$180 . What does each item cost?

Solve by determinants: x+6y=13x+6 y=13x+6y=13 4x−3y=−294 x-3 y=-294x−3y=−29

Find the value of the second-order determinant: ∣xywz∣\left|\begin{array}{ll}x & y \\ w & z\end{array}\right|​xw​yz​​

Solve by determinants: 1.02x−2.03y=9.161.02 x-2.03 y=9.161.02x−2.03y=9.16 -2.05x+3.04z=-4.17 -1.04y-2.05z=-2.02

Evaluate the determinant: ∣3−240−24−31−2∣\left|\begin{array}{ccc}3 & -2 & 4 \\ 0 & -2 & 4 \\ -3 & 1 & -2\end{array}\right|​30−3​−2−21​44−2​​

Solve by determinants: 2x−4y=62 x-4 y=62x−4y=6 5x−y=95 x-y=95x−y=9

Evaluate the determinant: ∣3140−23−16013−104−52∣\left|\begin{array}{cccc}3 & 1 & 4 & 0 \\ -2 & 3 & -1 & 6 \\ 0 & 1 & 3 & -1 \\ 0 & 4 & -5 & 2\end{array}\right|​3−200​1314​4−13−5​06−12​​

Solve by determinants: 3x−5y+14z=−553 x-5 y+14 z=-553x−5y+14z=−55 10x+2y-7z =43 2x-y+z =-10

Evaluate the determinant: ∣0524012−8401227111∣\left|\begin{array}{cccc}0 & 5 & 2 & 4 \\ 0 & 1 & 2 & -8 \\ 4 & 0 & 12 & 2 \\ 7 & 1 & 1 & 1\end{array}\right|​0047​5101​22121​4−821​​

Solve by determinants: 1x+1y−1z=−2\frac{1}{x}+\frac{1}{y}-\frac{1}{z}=-2x1​+y1​−z1​=−2 -+=13 ++=9

Find the value of the second-order determinant: ∣3a52a−6∣\left|\begin{array}{cc}3 a & 5 \\ 2 a & -6\end{array}\right|​3a2a​5−6​​

Solve by determinants: 2x=3y+182 x=3 y+182x=3y+18 y=5−3xy=5-3 xy=5−3x

Solve by determinants: x+y−2z=14x+y-2 z=14x+y−2z=14 2x-y+3z =-10 2x+3y-2z =8

Solve by determinants: 2x+4y=162 x+4 y=162x+4y=16 3x−2y=−83 x-2 y=-83x−2y=−8

Solve by determinants: x+y+z=6x+y+z=6x+y+z=6 -x+y =-8 x-z =1

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Filters

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

Solve by determinants: $x-2 y+z=3$ 2x+2y-3z=9 2x-3y+z=-9

Solve by determinants: $2 x-y=1$ 4y-z=3 x-3z=-2

A shipment of 10 calculators and 8 flash drives cost $\$ 246$ . Another shipment of 4 calculators and 10 flash drives cost $\$ 180$ . What does each item cost?

Solve by determinants: $x+6 y=13$ $4 x-3 y=-29$

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

Solve by determinants: $1.02 x-2.03 y=9.16$ -2.05x+3.04z=-4.17 -1.04y-2.05z=-2.02

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

Solve by determinants: $2 x-4 y=6$ $5 x-y=9$

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

Solve by determinants: $3 x-5 y+14 z=-55$ 10x+2y-7z =43 2x-y+z =-10

Evaluate the determinant: $\left|\begin{array}{cccc}0 & 5 & 2 & 4 \\ 0 & 1 & 2 & -8 \\ 4 & 0 & 12 & 2 \\ 7 & 1 & 1 & 1\end{array}\right|$

Solve by determinants: $\frac{1}{x}+\frac{1}{y}-\frac{1}{z}=-2$ -+=13 ++=9

Find the value of the second-order determinant: $\left|\begin{array}{cc}3 a & 5 \\ 2 a & -6\end{array}\right|$

Solve by determinants: $2 x=3 y+18$ $y=5-3 x$

Solve by determinants: $x+y-2 z=14$ 2x-y+3z =-10 2x+3y-2z =8

Solve by determinants: $2 x+4 y=16$ $3 x-2 y=-8$

Solve by determinants: $x+y+z=6$ -x+y =-8 x-z =1